X-Git-Url: http://git.hungrycats.org/cgi-bin/gitweb.cgi?a=blobdiff_plain;f=hacks%2Fxlyap.c;fp=hacks%2Fxlyap.c;h=350888d0c379a45f6e3fab3acb65c6bb7070f247;hb=5b7bc6e70fb439cf4c4bf771ae9f94077fe4fe08;hp=0000000000000000000000000000000000000000;hpb=186b0b9f1638444c650c9273df38085e0db71e4a;p=xscreensaver

diff --git a/hacks/xlyap.c b/hacks/xlyap.c
new file mode 100644
index 00000000..350888d0
--- /dev/null
+++ b/hacks/xlyap.c
@@ -0,0 +1,1965 @@
+/* Lyap - calculate and display Lyapunov exponents */
+
+/* Written by Ron Record (rr@sco) 03 Sep 1991 */
+
+/* The idea here is to calculate the Lyapunov exponent for a periodically
+ * forced logistic map (later i added several other nonlinear maps of the unit
+ * interval). In order to turn the 1-dimensional parameter space of the
+ * logistic map into a 2-dimensional parameter space, select two parameter
+ * values ('a' and 'b') then alternate the iterations of the logistic map using
+ * first 'a' then 'b' as the parameter. This program accepts an argument to
+ * specify a forcing function, so instead of just alternating 'a' and 'b', you
+ * can use 'a' as the parameter for say 6 iterations, then 'b' for 6 iterations
+ * and so on. An interesting forcing function to look at is abbabaab (the
+ * Morse-Thue sequence, an aperiodic self-similar, self-generating sequence).
+ * Anyway, step through all the values of 'a' and 'b' in the ranges you want,
+ * calculating the Lyapunov exponent for each pair of values. The exponent
+ * is calculated by iterating out a ways (specified by the variable "settle")
+ * then on subsequent iterations calculating an average of the logarithm of
+ * the absolute value of the derivative at that point. Points in parameter
+ * space with a negative Lyapunov exponent are colored one way (using the
+ * value of the exponent to index into a color map) while points with a
+ * non-negative exponent are colored differently.
+ *
+ * The algorithm was taken from the September 1991 Scientific American article
+ * by A. K. Dewdney who gives credit to Mario Markus of the Max Planck Institute
+ * for its creation. Additional information and ideas were gleaned from the
+ * discussion on alt.fractals involving Stephen Hall, Ed Kubaitis, Dave Platt
+ * and Baback Moghaddam. Assistance with colormaps and spinning color wheels
+ * and X was gleaned from Hiram Clawson. Rubber banding code was adapted from
+ * an existing Mandelbrot program written by Stacey Campbell.
+ */
+
+#define LYAP_PATCHLEVEL 4
+#define LYAP_VERSION "#(@) lyap 2.3 2/20/92"
+
+#include <assert.h>
+#include <math.h>
+
+#include "screenhack.h"
+#include "yarandom.h"
+#include "hsv.h"
+#include "vroot.h"
+
+#include <X11/cursorfont.h> 
+#include <X11/Xutil.h> 
+
+char *progclass = "XLyap";
+
+char *defaults [] = {
+  "XLyap.background:	black",		/* to placate SGI */
+  "*randomize:		false",
+  "*builtin:		-1",
+  "*minColor:		1",
+  "*maxColor:		256",
+  "*dwell:		50",
+  "*useLog:		false",
+  "*colorExponent:	1.0",
+  "*colorOffset:	0",
+  "*randomForce:	",		/* 0.5 */
+  "*settle:		50",
+  "*minA:		2.0",
+  "*minB:		2.0",
+  "*wheels:		7",
+  "*function:		10101010",
+  "*forcingFunction:	abbabaab",
+  "*bRange:		",		/* 2.0 */
+  "*startX:		0.65",
+  "*mapIndex:		",		/* 0 */
+  "*outputFile:		",
+  "*beNegative:		false",
+  "*rgbMax:		65000",
+  "*spinLength:		256",
+  "*show:		false",
+  "*aRange:		",		/* 2.0 */
+  0
+};
+
+XrmOptionDescRec options [] = {
+  { "-randomize", ".randomize",	XrmoptionNoArg, "true" },
+  { "-builtin",   ".builtin",	XrmoptionSepArg, 0 },
+  { "-C", ".minColor",		XrmoptionSepArg, 0 },	/* n */
+  { "-D", ".dwell",		XrmoptionSepArg, 0 },	/* n */
+  { "-L", ".useLog",		XrmoptionNoArg, "true" },
+  { "-M", ".colorExponent",	XrmoptionSepArg, 0 },	/* r */
+  { "-O", ".colorOffset",	XrmoptionSepArg, 0 },	/* n */
+  { "-R", ".randomForce",	XrmoptionSepArg, 0 },	/* p */
+  { "-S", ".settle",		XrmoptionSepArg, 0 },	/* n */
+  { "-a", ".minA",		XrmoptionSepArg, 0 },	/* r */
+  { "-b", ".minB",		XrmoptionSepArg, 0 },	/* n */
+  { "-c", ".wheels",		XrmoptionSepArg, 0 },	/* n */
+  { "-F", ".function",		XrmoptionSepArg, 0 },	/* 10101010 */
+  { "-f", ".forcingFunction",	XrmoptionSepArg, 0 },	/* abbabaab */
+  { "-h", ".bRange",		XrmoptionSepArg, 0 },	/* r */
+  { "-i", ".startX",		XrmoptionSepArg, 0 },	/* r */
+  { "-m", ".mapIndex",		XrmoptionSepArg, 0 },	/* n */
+  { "-o", ".outputFile",	XrmoptionSepArg, 0 },	/* filename */
+  { "-p", ".beNegative",	XrmoptionNoArg, "true" },
+  { "-r", ".rgbMax",		XrmoptionSepArg, 0 },	/* n */
+  { "-s", ".spinLength",	XrmoptionSepArg, 0 },	/* n */
+  { "-v", ".show",		XrmoptionNoArg, "true" },
+  { "-w", ".aRange",		XrmoptionSepArg, 0 },	/* r */
+  { 0, 0, 0, 0 }
+};
+
+
+#define ABS(a)	(((a)<0) ? (0-(a)) : (a) )
+#define Min(x,y) ((x < y)?x:y)
+#define Max(x,y) ((x > y)?x:y)
+
+#ifdef SIXTEEN_COLORS
+#define MAXPOINTS  128
+#define MAXFRAMES 4
+#define MAXCOLOR 16
+static int maxcolor=16, startcolor=0, color_offset=0, mincolindex=1;
+static int dwell=50, settle=25;
+static int width=128, height=128, xposition=128, yposition=128;
+#else
+#define MAXPOINTS  256
+#define MAXFRAMES 8
+#define MAXCOLOR 256
+static int maxcolor=256, startcolor=17, color_offset=96, mincolindex=33;
+static int dwell=100, settle=50;
+static int width=256, height=256;
+#endif
+
+#ifndef TRUE
+#define TRUE 1
+#define FALSE 0
+#endif
+
+static int screen;
+static Display*	dpy;
+static Visual *visual;
+
+static unsigned long foreground, background;
+
+static Window canvas;
+
+typedef struct {
+	int x, y;
+} xy_t;
+
+typedef struct {
+	int start_x, start_y;
+	int last_x, last_y;
+	} rubber_band_data_t;
+
+typedef struct {
+	Cursor band_cursor;
+	double p_min, p_max, q_min, q_max;
+	rubber_band_data_t rubber_band;
+	} image_data_t;
+
+typedef struct points_t {
+	XPoint data[MAXCOLOR][MAXPOINTS];
+	int npoints[MAXCOLOR];
+	} points_t;
+
+static points_t Points;
+static image_data_t rubber_data;
+
+#ifndef TRUE
+#define TRUE 1
+#define FALSE 0
+#endif
+
+static GC Data_GC[MAXCOLOR], RubberGC;
+
+#define MAXINDEX 64
+#define FUNCMAXINDEX 16
+#define MAXWHEELS 7
+#define NUMMAPS 5
+
+typedef double (*PFD)(double,double);
+
+static double logistic(double,double), circle(double,double), leftlog(double,double), rightlog(double,double), doublelog(double,double);
+static double dlogistic(double,double), dcircle(double,double), dleftlog(double,double), drightlog(double,double), ddoublelog(double,double);
+static PFD map, deriv;
+static PFD Maps[NUMMAPS] = { logistic, circle, leftlog, rightlog, doublelog };
+static PFD Derivs[NUMMAPS] = { dlogistic, dcircle, dleftlog, drightlog, ddoublelog };
+
+static int aflag=0, bflag=0, wflag=0, hflag=0, Rflag=0;
+static double pmins[NUMMAPS] = { 2.0, 0.0, 0.0, 0.0, 0.0 };
+static double pmaxs[NUMMAPS] = { 4.0, 1.0, 6.75, 6.75, 16.0 };
+static double amins[NUMMAPS] = { 2.0, 0.0, 0.0, 0.0, 0.0 };
+static double aranges[NUMMAPS] = { 2.0, 1.0, 6.75, 6.75, 16.0 };
+static double bmins[NUMMAPS] = { 2.0, 0.0, 0.0, 0.0, 0.0 };
+static double branges[NUMMAPS] = { 2.0, 1.0, 6.75, 6.75, 16.0 };
+
+static int   forcing[MAXINDEX] = { 0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,
+			0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,
+			0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1 };
+static int   Forcing[FUNCMAXINDEX] = { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 };
+
+static int   maxindex = MAXINDEX;
+static int   funcmaxindex = FUNCMAXINDEX;
+static double	min_a=2.0, min_b=2.0, a_range=2.0, b_range=2.0, minlyap=1.0;
+static double  max_a=4.0, max_b=4.0;
+static double  start_x=0.65, lyapunov, a_inc, b_inc, a, b;
+static int	numcolors=16, numfreecols, displayplanes, lowrange;
+static xy_t	point;
+static Pixmap  pixmap;
+static Colormap cmap;
+static XColor	Colors[MAXCOLOR];
+static double  *exponents[MAXFRAMES];
+static double  a_minimums[MAXFRAMES], b_minimums[MAXFRAMES];
+static double  a_maximums[MAXFRAMES], b_maximums[MAXFRAMES];
+static double  minexp, maxexp, prob=0.5;
+static int     expind[MAXFRAMES]={0}, resized[MAXFRAMES]={0};
+static int	numwheels=MAXWHEELS, force=0, Force=0, negative=1;
+static int     rgb_max=65000, nostart=1, stripe_interval=7;
+static int	save=1, show=0, useprod=1, spinlength=256, savefile=0;
+static int	maxframe=0, frame=0, dorecalc=0, mapindex=0, run=1;
+static char	*outname="lyap.out";
+
+
+const char * const version = LYAP_VERSION;
+
+static void resize(void);
+static void redisplay(Window w, XExposeEvent *event);
+static void Spin(Window w);
+static void show_defaults(void);
+static void StartRubberBand(Window w, image_data_t *data, XEvent *event);
+static void TrackRubberBand(Window w, image_data_t *data, XEvent *event);
+static void EndRubberBand(Window w, image_data_t *data, XEvent *event);
+static void CreateXorGC(void);
+static void InitBuffer(void);
+static void BufferPoint(Display *display, Window window, int color,
+			int x, int y);
+static void FlushBuffer(void);
+static void init_canvas(void);
+static void init_data(void);
+static void init_color(void);
+static void parseargs(void);
+static void Clear(void);
+static void setupmem(void);
+static void main_event(void);
+static int complyap(void);
+static void Getkey(XKeyEvent *event);
+static int sendpoint(double expo);
+static void save_to_file(void);
+static void setforcing(void);
+static void check_params(int mapnum, int parnum);
+static void usage(void);
+static void Destroy_frame(void);
+static void freemem(void);
+static void Redraw(void);
+static void redraw(double *exparray, int index, int cont);
+static void recalc(void);
+static void SetupCorners(XPoint *corners, image_data_t *data);
+static void set_new_params(Window w, image_data_t *data);
+static void go_down(void);
+static void go_back(void);
+static void go_init(void);
+static void jumpwin(void);
+static void print_help(void);
+static void print_values(void);
+
+
+void
+screenhack (Display *d, Window window)
+{
+  XWindowAttributes xgwa;
+  int builtin = -1;
+  dpy = d;
+  XGetWindowAttributes (dpy, window, &xgwa);
+  width = xgwa.width;
+  height = xgwa.height;
+  visual = xgwa.visual;
+  cmap = xgwa.colormap;
+
+  parseargs();
+
+  if (get_boolean_resource("randomize", "Boolean"))
+    builtin = random() % 22;
+  else {
+    char *s = get_string_resource("builtin", "Integer");
+    if (s && *s)
+      builtin = atoi(s);
+    if (s) free (s);
+  }
+    
+  if (builtin >= 0)
+    {
+      char *ff = 0;
+      switch (builtin) {
+      case 0:
+	min_a = 3.75; aflag++;
+	min_b = 3.299999; bflag++;
+	a_range = 0.05; wflag++;
+	b_range = 0.05; hflag++;
+	dwell = 200;
+	settle = 100;
+	ff = "abaabbaaabbb";
+	break;
+
+      case 1:
+	min_a = 3.8; aflag++;
+	min_b = 3.2; bflag++;
+	b_range = .05; hflag++;
+	a_range = .05; wflag++;
+	ff = "bbbbbaaaaa";
+	break;
+
+      case 2:
+	min_a =  3.4; aflag++;
+	min_b =  3.04; bflag++;
+	a_range =  .5; wflag++;
+	b_range =  .5; hflag++;
+	ff = "abbbbbbbbb";
+	settle = 500;
+	dwell = 1000;
+	break;
+
+      case 3:
+	min_a = 3.5; aflag++;
+	min_b = 3.0; bflag++;
+	a_range = 0.2; wflag++;
+	b_range = 0.2; hflag++;
+	dwell = 600;
+	settle = 300;
+	ff = "aaabbbab";
+	break;
+
+      case 4:
+	min_a = 3.55667; aflag++;
+	min_b = 3.2; bflag++;
+	b_range = .05; hflag++;
+	a_range = .05; wflag++;
+	ff = "bbbbbaaaaa";
+	break;
+
+      case 5:
+	min_a = 3.79; aflag++;
+	min_b = 3.22; bflag++;
+	b_range = .02999; hflag++;
+	a_range = .02999; wflag++;
+	ff = "bbbbbaaaaa";
+	break;
+
+      case 6:
+	min_a = 3.7999; aflag++;
+	min_b = 3.299999; bflag++;
+	a_range = 0.2; wflag++;
+	b_range = 0.2; hflag++;
+	dwell = 300;
+	settle = 150;
+	ff = "abaabbaaabbb";
+	break;
+
+      case 7:
+	min_a = 3.89; aflag++;
+	min_b = 3.22; bflag++;
+	b_range = .028; hflag++;
+	a_range = .02999; wflag++;
+	ff = "bbbbbaaaaa";
+	settle = 600;
+	dwell = 1000;
+	break;
+
+      case 8:
+	min_a = 3.2; aflag++;
+	min_b = 3.7; bflag++;
+	a_range = 0.05; wflag++;
+	b_range = .005; hflag++;
+	ff = "abbbbaa";
+	break;
+
+      case 9:
+	ff = "aaaaaabbbbbb";
+	mapindex = 1;
+	dwell =  400;
+	settle =  200;
+	minlyap = maxexp = ABS(-0.85);
+	minexp = -1.0 * minlyap;
+	break;
+
+      case 10:
+	ff = "aaaaaabbbbbb";
+	mapindex = 1;
+	dwell =  400;
+	settle = 200;
+	minlyap = maxexp = ABS(-0.85);
+	minexp = -1.0 * minlyap;
+	break;
+
+      case 11:
+	mapindex = 1;
+	dwell =  400;
+	settle = 200;
+	minlyap = maxexp = ABS(-0.85);
+	minexp = -1.0 * minlyap;
+	break;
+
+      case 12:
+	ff = "abbb";
+	mapindex = 1;
+	dwell =  400;
+	settle = 200;
+	minlyap = maxexp = ABS(-0.85);
+	minexp = -1.0 * minlyap;
+	break;
+
+      case 13:
+	ff = "abbabaab";
+	mapindex = 1;
+	dwell =  400;
+	settle = 200;
+	minlyap = maxexp = ABS(-0.85);
+	minexp = -1.0 * minlyap;
+	break;
+
+      case 14:
+	ff = "abbabaab";
+	dwell =  800;
+	settle = 200;
+	minlyap = maxexp = ABS(-0.85);
+	minexp = -1.0 * minlyap;
+	/* ####  -x 0.05 */
+	min_a = 3.91; aflag++;
+	a_range =  0.0899999999; wflag++;
+	min_b =  3.28; bflag++;
+	b_range =  0.35; hflag++;
+	break;
+
+      case 15:
+	ff = "aaaaaabbbbbb";
+	dwell =  400;
+	settle = 200;
+	minlyap = maxexp = ABS(-0.85);
+	minexp = -1.0 * minlyap;
+	break;
+
+      case 16:
+	dwell =  400;
+	settle = 200;
+	minlyap = maxexp = ABS(-0.85);
+	minexp = -1.0 * minlyap;
+	break;
+
+      case 17:
+	ff = "abbb";
+	dwell =  400;
+	settle = 200;
+	minlyap = maxexp = ABS(-0.85);
+	minexp = -1.0 * minlyap;
+	break;
+
+      case 18:
+	ff = "abbabaab";
+	dwell =  400;
+	settle = 200;
+	minlyap = maxexp = ABS(-0.85);
+	minexp = -1.0 * minlyap;
+	break;
+
+      case 19:
+	mapindex = 2;
+	ff = "aaaaaabbbbbb";
+	dwell =  400;
+	settle = 200;
+	minlyap = maxexp = ABS(-0.85);
+	minexp = -1.0 * minlyap;
+	break;
+
+      case 20:
+	mapindex = 2;
+	dwell =  400;
+	settle = 200;
+	minlyap = maxexp = ABS(-0.85);
+	minexp = -1.0 * minlyap;
+	break;
+
+      case 21:
+	mapindex = 2;
+	ff = "abbb";
+	dwell =  400;
+	settle = 200;
+	minlyap = maxexp = ABS(-0.85);
+	minexp = -1.0 * minlyap;
+	break;
+
+      case 22:
+	mapindex = 2;
+	ff = "abbabaab";
+	dwell =  400;
+	settle = 200;
+	minlyap = maxexp = ABS(-0.85);
+	minexp = -1.0 * minlyap;
+	break;
+      }
+
+      if (ff) {
+	char *ch;
+	int bindex = 0;
+	maxindex = strlen(ff);
+	if (maxindex > MAXINDEX)
+	  usage();
+	ch = ff;
+	force++;
+	while (bindex < maxindex) {
+	  if (*ch == 'a')
+	    forcing[bindex++] = 0;
+	  else if (*ch == 'b')
+	    forcing[bindex++] = 1;
+	  else
+	    usage();
+	  ch++;
+	}
+      }
+    }
+
+  screen = DefaultScreen(dpy);
+  background = BlackPixel(dpy, screen);
+  setupmem();
+  init_data();
+  if (displayplanes > 1)
+    foreground = startcolor;
+  else
+    foreground = WhitePixel(dpy, screen);
+
+  /*
+  * Create the window to display the Lyapunov exponents
+  */
+  canvas = window;
+  init_canvas();
+
+  if (window != DefaultRootWindow(dpy))
+    XSelectInput(dpy,canvas,KeyPressMask|ButtonPressMask|ButtonMotionMask|
+		 ButtonReleaseMask|ExposureMask|StructureNotifyMask);
+  if (displayplanes > 1) {
+    init_color();
+  } else {
+    XQueryColors(dpy, DefaultColormap(dpy, DefaultScreen(dpy)),
+	Colors, numcolors);
+  }
+  pixmap = XCreatePixmap(dpy, DefaultRootWindow(dpy),
+			 width, height, DefaultDepth(dpy, screen));
+  rubber_data.band_cursor = XCreateFontCursor(dpy, XC_hand2);
+  CreateXorGC();
+  Clear();
+  for(;;)
+      main_event();
+}
+
+static void
+main_event(void)
+{
+  int n;
+  XEvent event;
+
+  if (complyap() == TRUE)
+      run=0;
+  n = XEventsQueued(dpy, QueuedAfterFlush);
+  while (n--) {
+	  XNextEvent(dpy, &event);
+	    switch(event.type)
+	    {
+	    case KeyPress:
+    Getkey(&event.xkey);
+    break;
+	    case Expose:
+    redisplay(canvas, &event.xexpose);
+	  break;
+	    case ConfigureNotify:
+    resize();
+	  break;
+	    case ButtonPress:
+    StartRubberBand(canvas, &rubber_data, &event);
+	  break;
+	    case MotionNotify:
+    TrackRubberBand(canvas, &rubber_data, &event);
+	  break;
+	    case ButtonRelease:
+    EndRubberBand(canvas, &rubber_data, &event);
+	  break;
+	    }
+	}
+}
+
+/* complyap() is the guts of the program. This is where the Lyapunov exponent
+ * is calculated. For each iteration (past some large number of iterations)
+ * calculate the logarithm of the absolute value of the derivative at that
+ * point. Then average them over some large number of iterations. Some small
+ * speed up is achieved by utilizing the fact that log(a*b) = log(a) + log(b).
+ */
+static int
+complyap(void)
+{
+  register i, bindex;
+  double total, prod, x, r;
+
+  if (!run)
+    return TRUE;
+  a += a_inc;
+  if (a >= max_a)
+    if (sendpoint(lyapunov) == TRUE)
+      return FALSE;
+    else {
+      FlushBuffer();
+      if (savefile)
+	save_to_file();
+      return TRUE;
+    }
+  if (b >= max_b) {
+    FlushBuffer();
+    if (savefile)
+      save_to_file();
+    return TRUE;
+  }
+  prod = 1.0;
+  total = 0.0;
+  bindex = 0;
+  x = start_x;
+  r = (forcing[bindex]) ? b : a;
+#ifdef MAPS
+  findex = 0;
+  map = Maps[Forcing[findex]];
+#endif
+  for (i=0;i<settle;i++) {     /* Here's where we let the thing */
+    x = (*map)(x, r);	 /* "settle down". There is usually */
+    if (++bindex >= maxindex) { /* some initial "noise" in the */
+      bindex = 0;    /* iterations. How can we optimize */
+      if (Rflag)      /* the value of settle ??? */
+	  setforcing();
+    }
+    r = (forcing[bindex]) ? b : a;
+#ifdef MAPS
+    if (++findex >= funcmaxindex)
+      findex = 0;
+    map = Maps[Forcing[findex]];
+#endif
+  }
+#ifdef MAPS
+  deriv = Derivs[Forcing[findex]];
+#endif
+  if (useprod) {      /* using log(a*b) */
+    for (i=0;i<dwell;i++) {
+      x = (*map)(x, r);
+      prod *= ABS((*deriv)(x, r));
+      /* we need to prevent overflow and underflow */
+      if ((prod > 1.0e12) || (prod < 1.0e-12)) {
+	total += log(prod);
+	prod = 1.0;
+      }
+      if (++bindex >= maxindex) {
+	bindex = 0;
+	if (Rflag)
+	  setforcing();
+      }
+      r = (forcing[bindex]) ? b : a;
+#ifdef MAPS
+      if (++findex >= funcmaxindex)
+	findex = 0;
+      map = Maps[Forcing[findex]];
+      deriv = Derivs[Forcing[findex]];
+#endif
+    }
+    total += log(prod);
+    lyapunov = (total * M_LOG2E) / (double)dwell;
+  }
+  else {	/* use log(a) + log(b) */
+    for (i=0;i<dwell;i++) {
+      x = (*map)(x, r);
+      total += log(ABS((*deriv)(x, r)));
+      if (++bindex >= maxindex) {
+	bindex = 0;
+	if (Rflag)
+	  setforcing();
+      }
+      r = (forcing[bindex]) ? b : a;
+#ifdef MAPS
+      if (++findex >= funcmaxindex)
+	findex = 0;
+      map = Maps[Forcing[findex]];
+      deriv = Derivs[Forcing[findex]];
+#endif
+    }
+    lyapunov = (total * M_LOG2E) / (double)dwell;
+  }
+  if (sendpoint(lyapunov) == TRUE)
+    return FALSE;
+  else {
+    FlushBuffer();
+    if (savefile)
+      save_to_file();
+    return TRUE;
+  }
+}
+
+static double
+logistic(double x, double r)	    /* the familiar logistic map */
+{
+  return(r * x * (1.0 - x));
+}
+
+static double
+dlogistic(double x, double r)	    /* the derivative of logistic map */
+{
+  return(r - (2.0 * r * x));
+}
+
+static double
+circle(double x, double r)	  /* sin() hump or sorta like the circle map */
+{
+  return(r * sin(M_PI * x));
+}
+
+static double
+dcircle(double x, double r)	  /* derivative of the "sin() hump" */
+{
+  return(r * M_PI * cos(M_PI * x));
+}
+
+static double
+leftlog(double x, double r)	  /* left skewed logistic */
+{
+  double d;
+
+  d = 1.0 - x;
+  return(r * x * d * d);
+}
+
+static double
+dleftlog(double x, double r)    /* derivative of the left skewed logistic */
+{
+  return(r * (1.0 - (4.0 * x) + (3.0 * x * x)));
+}
+
+static double
+rightlog(double x, double r)    /* right skewed logistic */
+{
+  return(r * x * x * (1.0 - x));
+}
+
+static double
+drightlog(double x, double r)    /* derivative of the right skewed logistic */
+{
+  return(r * ((2.0 * x) - (3.0 * x * x)));
+}
+
+static double
+doublelog(double x, double r)    /* double logistic */
+{
+  double d;
+
+  d = 1.0 - x;
+  return(r * x * x * d * d);
+}
+
+static double
+ddoublelog(double x, double r)   /* derivative of the double logistic */
+{
+  double d;
+
+  d = x * x;
+  return(r * ((2.0 * x) - (6.0 * d) + (4.0 * x * d)));
+}
+
+static void
+init_data(void)
+{
+  numcolors = XDisplayCells(dpy, XDefaultScreen(dpy));
+  displayplanes = DisplayPlanes(dpy, XDefaultScreen(dpy));
+  if (numcolors > maxcolor)
+    numcolors = maxcolor;
+  numfreecols = numcolors - mincolindex;
+  lowrange = mincolindex - startcolor;
+  a_inc = a_range / (double)width;
+  b_inc = b_range / (double)height;
+  point.x = -1;
+  point.y = 0;
+  a = rubber_data.p_min = min_a;
+  b = rubber_data.q_min = min_b;
+  rubber_data.p_max = max_a;
+  rubber_data.q_max = max_b;
+  if (show)
+    show_defaults();
+  InitBuffer();
+  ya_rand_init(0);
+}
+
+static void
+init_canvas(void)
+{
+  static int i;
+
+  /*
+  * create default, writable, graphics contexts for the canvas.
+  */
+	for (i=0; i<maxcolor; i++) {
+	    Data_GC[i] = XCreateGC(dpy, DefaultRootWindow(dpy),
+		(unsigned long) NULL, (XGCValues *) NULL);
+	    /* set the background to black */
+	    XSetBackground(dpy,Data_GC[i],BlackPixel(dpy,XDefaultScreen(dpy)));
+	    /* set the foreground of the ith context to i */
+	    XSetForeground(dpy, Data_GC[i], i);
+	}
+	if (displayplanes == 1) {
+	    XSetForeground(dpy,Data_GC[0],BlackPixel(dpy,XDefaultScreen(dpy)));
+	    XSetForeground(dpy,Data_GC[1],WhitePixel(dpy,XDefaultScreen(dpy)));
+	}
+}
+
+#if 0
+static void
+hls2rgb(int hue_light_sat[3],
+	int rgb[3])		/*	Each in range [0..65535]	*/
+{
+  unsigned short r, g, b;
+  hsv_to_rgb((int) (hue_light_sat[0] / 10),		/* 0-3600 -> 0-360 */
+	     (int) ((hue_light_sat[2]/1000.0) * 64435), /* 0-1000 -> 0-65535 */
+	     (int) ((hue_light_sat[1]/1000.0) * 64435), /* 0-1000 -> 0-65535 */
+	     &r, &g, &b);
+  rgb[0] = r;
+  rgb[1] = g;
+  rgb[2] = b;
+}
+#endif /* 0 */
+
+
+static void
+init_color(void)
+{
+#if 1
+
+  int i;
+  XColor colors[256];
+  int ncolors = maxcolor;
+  Bool writable = False;
+  make_smooth_colormap(dpy, visual, cmap,
+			colors, &ncolors, True, &writable, True);
+
+  for (i = 0; i < maxcolor; i++)
+    XSetForeground(dpy, Data_GC[i],
+		   colors[((int) ((i / ((float)maxcolor)) * ncolors))].pixel);
+
+#else
+  static int i, j, colgap, leg, step;
+  static Visual *visual;
+  Colormap def_cmap;
+  int hls[3], rgb[3];
+
+  def_cmap = DefaultColormap(dpy, DefaultScreen(dpy));
+  for (i=0; i<numcolors; i++) {
+    Colors[i].pixel = i;
+    Colors[i].flags = DoRed|DoGreen|DoBlue;
+  }
+
+  /* Try to write into a new color map */
+  visual = DefaultVisual(dpy, DefaultScreen(dpy));
+  cmap = XCreateColormap(dpy, canvas, visual, AllocAll);
+  XQueryColors(dpy, def_cmap, Colors, numcolors);
+  if (mincolindex)
+    colgap = rgb_max / mincolindex;
+  else
+    colgap = rgb_max;
+  hls[0] = 50;	/* Hue in low range */
+  hls[2] = 1000;  /* Fully saturated */
+  for (i=startcolor; i<lowrange + startcolor; i++) {
+    hls[1] = 1000L * (i-startcolor) / lowrange;
+    hls2rgb(hls, rgb);
+    Colors[i].red = rgb[0];
+    Colors[i].green = rgb[1];
+    Colors[i].blue = rgb[2];
+  }
+  colgap = rgb_max / numcolors;
+  if (numwheels == 0)
+    XQueryColors(dpy, def_cmap, Colors, numcolors);
+  else if (numwheels == 1) {
+    colgap = 2*rgb_max/(numcolors - color_offset);
+    for (i=mincolindex; i<(numcolors/2); i++) {
+      Colors[i].blue = 0;
+      Colors[i].green=((i+color_offset)*colgap);
+      Colors[i].red=((i+color_offset)*colgap);
+    }
+    for (i=(numcolors/2); i<(numcolors); i++) {
+      Colors[i].blue = 0;
+      Colors[i].green=(((numcolors-i)+color_offset)*colgap);
+      Colors[i].red=(((numcolors-i)+color_offset)*colgap);
+    }
+  }
+  else if (numwheels == 2) {
+	  hls[0] = 800; /* Hue in mid range */
+	  hls[2] = 1000;  /* Fully saturated */
+	  for (i=startcolor; i<lowrange + startcolor; i++) {
+      hls[1] = 1000L * (i-startcolor) / lowrange;
+      hls2rgb(hls, rgb);
+      Colors[i].red = rgb[0];
+      Colors[i].green = rgb[1];
+      Colors[i].blue = rgb[2];
+	  }
+    for (i=mincolindex; i<(numcolors/2); i++) {
+      Colors[i].blue = rgb_max;
+      Colors[i].green = 0;
+      Colors[i].red=(i*2*rgb_max/numcolors);
+    }
+    for (i=(numcolors/2); i<numcolors; i++) {
+      Colors[i].blue = rgb_max;
+      Colors[i].green = 0;
+      Colors[i].red=((numcolors - i)*2*rgb_max/numcolors);
+    }
+  }
+  else if (numwheels == 3) {
+	  hls[0] = 800; /* Hue in mid range */
+	  hls[2] = 1000;  /* Fully saturated */
+	  for (i=startcolor; i<lowrange + startcolor; i++) {
+      hls[1] = 1000L * (i-startcolor) / lowrange;
+      hls2rgb(hls, rgb);
+      Colors[i].red = rgb[0];
+      Colors[i].green = rgb[1];
+      Colors[i].blue = rgb[2];
+	  }
+    colgap = 4*rgb_max/numcolors;
+    for (i=mincolindex; i<(numcolors/4); i++) {
+      Colors[i].blue = rgb_max;
+      Colors[i].green = 0;
+      Colors[i].red=(i*colgap);
+    }
+    for (i=(numcolors/4); i<(numcolors/2); i++) {
+      Colors[i].red = rgb_max;
+      Colors[i].green = 0;
+      Colors[i].blue=((numcolors/2) - i) * colgap;
+    }
+    for (i=(numcolors/2); i<(0.75*numcolors); i++) {
+      Colors[i].red = rgb_max;
+      Colors[i].blue=(i * colgap);
+      Colors[i].green = 0;
+    }
+    for (i=(0.75*numcolors); i<numcolors; i++) {
+      Colors[i].blue = rgb_max;
+      Colors[i].green = 0;
+      Colors[i].red=(numcolors-i)*colgap;
+    }
+  }
+  else if (numwheels == 4) {
+	  hls[0] = 800; /* Hue in mid range */
+	  hls[2] = 1000;  /* Fully saturated */
+	  for (i=startcolor; i<lowrange + startcolor; i++) {
+      hls[1] = 1000L * (i-startcolor) / lowrange;
+      hls2rgb(hls, rgb);
+      Colors[i].red = rgb[0];
+      Colors[i].green = rgb[1];
+      Colors[i].blue = rgb[2];
+	  }
+    colgap = numwheels * rgb_max / numcolors;
+    for (i=mincolindex; i<(numcolors/numwheels); i++) {
+      Colors[i].blue = rgb_max;
+      Colors[i].green = 0;
+      Colors[i].red=(i*colgap);
+    }
+    for (i=(numcolors/numwheels); i<(2*numcolors/numwheels); i++) {
+      Colors[i].red = rgb_max;
+      Colors[i].green = 0;
+      Colors[i].blue=((2*numcolors/numwheels) - i) * colgap;
+    }
+    for (i=(2*numcolors/numwheels); i<numcolors; i++) {
+      Colors[i].red = rgb_max;
+      Colors[i].green=(i - (2*numcolors/numwheels)) * colgap;
+      Colors[i].blue = 0;
+    }
+  }
+  else if (numwheels == 5) {
+    hls[1] = 700; /* Lightness in midrange */
+    hls[2] = 1000;  /* Fully saturated */
+    for (i=mincolindex; i<numcolors; i++) {
+      hls[0] = 3600L * i / numcolors;
+      hls2rgb(hls, rgb);
+      Colors[i].red = rgb[0];
+      Colors[i].green = rgb[1];
+      Colors[i].blue = rgb[2];
+    }
+    for (i=mincolindex; i<numcolors; i+=stripe_interval) {
+      hls[0] = 3600L * i / numcolors;
+      hls2rgb(hls, rgb);
+      Colors[i].red = rgb[0] / 2;
+      Colors[i].green = rgb[1] / 2;
+      Colors[i].blue = rgb[2] / 2;
+    }
+  }
+  else if (numwheels == 6) {
+      hls[0] = 800; /* Hue in mid range */
+      hls[2] = 1000;  /* Fully saturated */
+      for (i=startcolor; i<lowrange + startcolor; i++) {
+    hls[1] = 1000L * (i-startcolor) / lowrange;
+    hls2rgb(hls, rgb);
+    Colors[i].red = rgb[0];
+    Colors[i].green = rgb[1];
+    Colors[i].blue = rgb[2];
+      }
+      step = numfreecols / 3;
+      leg = step+mincolindex;
+      for (i = mincolindex; i < leg; ++i)
+      {
+    Colors[i].pixel = i;
+    Colors[i].red = fabs(65535 - (double)i / step * 65535.0);
+    Colors[i].blue = (double)i / step * 65535.0;
+    Colors[i].green = 0;
+    Colors[i].flags = DoRed | DoGreen | DoBlue;
+      }
+      for (j = 0, i = leg, leg += step; i < leg; ++i, ++j)
+      {
+    Colors[i].pixel = i;
+    Colors[i].red = (double)j / step * 65535.0;
+    Colors[i].blue = 65535;
+    Colors[i].green = Colors[i].red;
+    Colors[i].flags = DoRed | DoGreen | DoBlue;
+      }
+      for (j = 0, i = leg, leg += step; i < leg; ++i, ++j)
+      {
+    Colors[i].pixel = i;
+    Colors[i].red = 65535;
+    Colors[i].blue = fabs(65535 - (double)j / step * 65535.0);
+    Colors[i].green = Colors[i].blue;
+    Colors[i].flags = DoRed | DoGreen | DoBlue;
+      }
+  }
+  else if (numwheels == MAXWHEELS) {  /* rainbow palette */
+    hls[1] = 500; /* Lightness in midrange */
+    hls[2] = 1000;  /* Fully saturated */
+    for (i=mincolindex; i<numcolors; i++) {
+      hls[0] = 3600L * i / numcolors;
+      hls2rgb(hls, rgb);
+      Colors[i].red = rgb[0];
+      Colors[i].green = rgb[1];
+      Colors[i].blue = rgb[2];
+    }
+  }
+  XStoreColors(dpy, cmap, Colors, numcolors);
+
+  XSetWindowColormap(dpy, canvas, cmap);
+#endif
+}
+
+static void
+parseargs()
+{
+  static int i;
+  int bindex=0, findex;
+  char *s, *ch;
+
+  map = Maps[0];
+  deriv = Derivs[0];
+  maxexp=minlyap; minexp= -1.0 * minlyap;
+
+  mincolindex = get_integer_resource("minColor", "Integer");
+  dwell = get_integer_resource("dwell", "Integer");
+#ifdef MAPS
+  {
+    char *optarg = get_string_resource("function", "String");
+    funcmaxindex = strlen(optarg);
+    if (funcmaxindex > FUNCMAXINDEX)
+      usage();
+    ch = optarg;
+    Force++;
+    for (findex=0;findex<funcmaxindex;findex++) {
+      Forcing[findex] = (int)(*ch++ - '0');;
+      if (Forcing[findex] >= NUMMAPS)
+	usage();
+    }
+  }
+#endif
+  if (get_boolean_resource("useLog", "Boolean"))
+    useprod=0;
+
+  minlyap=ABS(get_float_resource("colorExponent", "Float"));
+  maxexp=minlyap;
+  minexp= -1.0 * minlyap;
+
+  color_offset = get_integer_resource("colorOffset", "Integer");
+
+  maxcolor=ABS(get_integer_resource("maxColor", "Integer"));
+  if ((maxcolor - startcolor) <= 0)
+    startcolor = 0;
+  if ((maxcolor - mincolindex) <= 0) {
+    mincolindex = 1;
+    color_offset = 0;
+  }
+
+  s = get_string_resource("randomForce", "Float");
+  if (s && *s) {
+    prob=atof(s); Rflag++; setforcing();
+  }
+
+  settle = get_integer_resource("settle", "Integer");
+
+  s = get_string_resource("minA", "Float");
+  if (s && *s) {
+    min_a = atof(s);
+    aflag++;
+  }
+  
+  s = get_string_resource("minB", "Float");
+  if (s && *s) {
+    min_b=atof(s); bflag++;
+  }
+  
+  numwheels = get_integer_resource("wheels", "Integer");
+
+  s = get_string_resource("forcingFunction", "String");
+  if (s && *s) {
+    maxindex = strlen(s);
+    if (maxindex > MAXINDEX)
+      usage();
+    ch = s;
+    force++;
+    while (bindex < maxindex) {
+      if (*ch == 'a')
+	forcing[bindex++] = 0;
+      else if (*ch == 'b')
+	forcing[bindex++] = 1;
+      else
+	usage();
+      ch++;
+    }
+  }
+
+  s = get_string_resource("bRange", "Float");
+  if (s && *s) {
+    b_range = atof(s);
+    hflag++;
+  }
+
+  start_x = get_float_resource("startX", "Float");
+
+  s = get_string_resource("mapIndex", "Integer");
+  if (s && *s) {
+    mapindex=atoi(s);
+    if ((mapindex >= NUMMAPS) || (mapindex < 0))
+      usage();
+    map = Maps[mapindex];
+    deriv = Derivs[mapindex];
+    if (!aflag)
+      min_a = amins[mapindex];
+    if (!wflag)
+      a_range = aranges[mapindex];
+    if (!bflag)
+      min_b = bmins[mapindex];
+    if (!hflag)
+      b_range = branges[mapindex];
+    if (!Force)
+      for (i=0;i<FUNCMAXINDEX;i++)
+	Forcing[i] = mapindex;
+  }
+
+  outname = get_string_resource("outputFile", "Integer");
+
+  if (get_boolean_resource("beNegative", "Boolean"))
+    negative--;
+
+  rgb_max = get_integer_resource("rgbMax", "Integer");
+  spinlength = get_integer_resource("spinLength", "Integer");
+  show = get_boolean_resource("show", "Boolean");
+
+  s = get_string_resource("aRange", "Float");
+  if (s && *s) {
+    a_range = atof(s); wflag++;
+  }
+
+  max_a = min_a + a_range;
+  max_b = min_b + b_range;
+
+  a_minimums[0] = min_a; b_minimums[0] = min_b;
+  a_maximums[0] = max_a; b_maximums[0] = max_b;
+
+  if (Force)
+    if (maxindex == funcmaxindex)
+      for (findex=0;findex<funcmaxindex;findex++)
+	check_params(Forcing[findex],forcing[findex]);
+    else
+      fprintf(stderr, "Warning! Unable to check parameters\n");
+  else
+    check_params(mapindex,2);
+}
+
+static void
+check_params(int mapnum, int parnum)
+{
+
+  if (parnum != 1) {
+      if ((max_a > pmaxs[mapnum]) || (min_a < pmins[mapnum])) {
+    fprintf(stderr, "Warning! Parameter 'a' out of range.\n");
+    fprintf(stderr, "You have requested a range of (%f,%f).\n",
+      min_a,max_a);
+    fprintf(stderr, "Valid range is (%f,%f).\n",
+      pmins[mapnum],pmaxs[mapnum]);
+      }
+  }
+  if (parnum != 0) {
+      if ((max_b > pmaxs[mapnum]) || (min_b < pmins[mapnum])) {
+    fprintf(stderr, "Warning! Parameter 'b' out of range.\n");
+    fprintf(stderr, "You have requested a range of (%f,%f).\n",
+      min_b,max_b);
+    fprintf(stderr, "Valid range is (%f,%f).\n",
+      pmins[mapnum],pmaxs[mapnum]);
+      }
+  }
+}
+
+static void
+usage(void)
+{
+    fprintf(stderr,"lyap [-BLs][-W#][-H#][-a#][-b#][-w#][-h#][-x xstart]\n");
+    fprintf(stderr,"\t[-M#][-S#][-D#][-f string][-r#][-O#][-C#][-c#][-m#]\n");
+#ifdef MAPS
+    fprintf(stderr,"\t[-F string]\n");
+#endif
+    fprintf(stderr,"\tWhere: -C# specifies the minimum color index\n");
+    fprintf(stderr,"\t	     -r# specifies the maxzimum rgb value\n");
+    fprintf(stderr,"\t	     -u displays this message\n");
+    fprintf(stderr,"\t	     -a# specifies the minimum horizontal parameter\n");
+    fprintf(stderr,"\t	     -b# specifies the minimum vertical parameter\n");
+    fprintf(stderr,"\t	     -w# specifies the horizontal parameter range\n");
+    fprintf(stderr,"\t	     -h# specifies the vertical parameter range\n");
+    fprintf(stderr,"\t	     -D# specifies the dwell\n");
+    fprintf(stderr,"\t	     -S# specifies the settle\n");
+    fprintf(stderr,"\t	     -H# specifies the initial window height\n");
+    fprintf(stderr,"\t	     -W# specifies the initial window width\n");
+    fprintf(stderr,"\t	     -O# specifies the color offset\n");
+    fprintf(stderr,"\t	     -c# specifies the desired color wheel\n");
+    fprintf(stderr,"\t	     -m# specifies the desired map (0-4)\n");
+    fprintf(stderr,"\t	     -f aabbb specifies a forcing function of 00111\n");
+#ifdef MAPS
+    fprintf(stderr,"\t	     -F 00111 specifies the function forcing function\n");
+#endif
+    fprintf(stderr,"\t	     -L indicates use log(x)+log(y) rather than log(xy)\n");
+    fprintf(stderr,"\tDuring display :\n");
+    fprintf(stderr,"\t	   Use the mouse to zoom in on an area\n");
+    fprintf(stderr,"\t	   e or E recalculates color indices\n");
+    fprintf(stderr,"\t	   f or F saves exponents to a file\n");
+    fprintf(stderr,"\t	   KJmn increase/decrease minimum negative exponent\n");
+    fprintf(stderr,"\t	   r or R redraws\n");
+    fprintf(stderr,"\t	   s or S spins the colorwheel\n");
+    fprintf(stderr,"\t	   w or W changes the color wheel\n");
+    fprintf(stderr,"\t	   x or X clears the window\n");
+    fprintf(stderr,"\t	   q or Q exits\n");
+    exit(1);
+}
+
+static void
+Cycle_frames(void)
+{
+  static int i;
+  for (i=0;i<=maxframe;i++)
+    redraw(exponents[i], expind[i], 1);
+}
+
+static void
+Spin(Window w)
+{
+  static int i, j;
+  long tmpxcolor;
+
+  if (displayplanes > 1) {
+    for (j=0;j<spinlength;j++) {
+      tmpxcolor = Colors[mincolindex].pixel;
+      for (i=mincolindex;i<numcolors-1;i++)
+	Colors[i].pixel = Colors[i+1].pixel;
+      Colors[numcolors-1].pixel = tmpxcolor;
+      XStoreColors(dpy, cmap, Colors, numcolors);
+    }
+    for (j=0;j<spinlength;j++) {
+      tmpxcolor = Colors[numcolors-1].pixel;
+      for (i=numcolors-1;i>mincolindex;i--)
+	Colors[i].pixel = Colors[i-1].pixel;
+      Colors[mincolindex].pixel = tmpxcolor;
+      XStoreColors(dpy, cmap, Colors, numcolors);
+    }
+  }
+}
+
+static void
+Getkey(XKeyEvent *event)
+{
+  unsigned char key;
+  static int i;
+  if (XLookupString(event, (char *)&key, sizeof(key), (KeySym *)0,
+	    (XComposeStatus *) 0) > 0)
+    switch (key) {
+  case '<': dwell /= 2; if (dwell < 1) dwell = 1; break;
+  case '>': dwell *= 2; break;
+  case '[': settle /= 2; if (settle < 1) settle = 1; break;
+  case ']': settle *= 2; break;
+  case 'd': go_down(); break;
+  case 'D': FlushBuffer(); break;
+  case 'e':
+  case 'E': FlushBuffer();
+      dorecalc = (!dorecalc);
+      if (dorecalc)
+      recalc();
+      else {
+      maxexp = minlyap; minexp = -1.0 * minlyap;
+      }
+      redraw(exponents[frame], expind[frame], 1);
+      break;
+  case 'f':
+  case 'F': save_to_file(); break;
+  case 'i': if (stripe_interval > 0) {
+      stripe_interval--;
+	if (displayplanes > 1) {
+	    init_color();
+	}
+      }
+      break;
+  case 'I': stripe_interval++;
+      if (displayplanes > 1) {
+	init_color();
+      }
+      break;
+  case 'K': if (minlyap > 0.05)
+      minlyap -= 0.05;
+       break;
+  case 'J': minlyap += 0.05;
+       break;
+  case 'm': mapindex++;
+		  if (mapindex >= NUMMAPS)
+			mapindex=0;
+		  map = Maps[mapindex];
+		  deriv = Derivs[mapindex];
+      if (!aflag)
+			min_a = amins[mapindex];
+		  if (!wflag)
+			a_range = aranges[mapindex];
+		  if (!bflag)
+			min_b = bmins[mapindex];
+		  if (!hflag)
+			b_range = branges[mapindex];
+		  if (!Force)
+			for (i=0;i<FUNCMAXINDEX;i++)
+			     Forcing[i] = mapindex;
+	    max_a = min_a + a_range;
+	    max_b = min_b + b_range;
+	    a_minimums[0] = min_a; b_minimums[0] = min_b;
+	    a_maximums[0] = max_a; b_maximums[0] = max_b;
+	    a_inc = a_range / (double)width;
+	    b_inc = b_range / (double)height;
+	    point.x = -1;
+	    point.y = 0;
+	    a = rubber_data.p_min = min_a;
+	    b = rubber_data.q_min = min_b;
+	    rubber_data.p_max = max_a;
+	    rubber_data.q_max = max_b;
+		  Clear();
+		  break;
+  case 'M': if (minlyap > 0.005)
+      minlyap -= 0.005;
+       break;
+  case 'N': minlyap += 0.005;
+       break;
+  case 'p':
+  case 'P': negative = (!negative);
+      FlushBuffer(); redraw(exponents[frame], expind[frame], 1);
+      break;
+  case 'r': FlushBuffer(); redraw(exponents[frame], expind[frame], 1);
+      break;
+  case 'R': FlushBuffer(); Redraw(); break;
+  case 's':
+       spinlength=spinlength/2;
+  case 'S': if (displayplanes > 1)
+      Spin(canvas);
+       spinlength=spinlength*2; break;
+  case 'u': go_back(); break;
+  case 'U': go_init(); break;
+  case 'v':
+  case 'V': print_values(); break;
+  case 'W': if (numwheels < MAXWHEELS)
+      numwheels++;
+       else
+      numwheels = 0;
+       if (displayplanes > 1) {
+	init_color();
+       }
+       break;
+  case 'w': if (numwheels > 0)
+      numwheels--;
+       else
+      numwheels = MAXWHEELS;
+       if (displayplanes > 1) {
+	init_color();
+       }
+       break;
+  case 'x': Clear(); break;
+  case 'X': Destroy_frame(); break;
+  case 'z': Cycle_frames(); redraw(exponents[frame], expind[frame], 1);
+      break;
+  case 'Z': while (!XPending(dpy)) Cycle_frames();
+      redraw(exponents[frame], expind[frame], 1); break;
+  case 'q':
+  case 'Q': exit(0); break;
+  case '?':
+  case 'h':
+  case 'H': print_help(); break;
+  default:  break;
+  }
+}
+
+/* Here's where we index into a color map. After the Lyapunov exponent is
+ * calculated, it is used to determine what color to use for that point.
+ * I suppose there are a lot of ways to do this. I used the following :
+ * if it's non-negative then there's a reserved area at the lower range
+ * of the color map that i index into. The ratio of some "minimum exponent
+ * value" and the calculated value is used as a ratio of how high to index
+ * into this reserved range. Usually these colors are dark red (see init_color).
+ * If the exponent is negative, the same ratio (expo/minlyap) is used to index
+ * into the remaining portion of the colormap (which is usually some light
+ * shades of color or a rainbow wheel). The coloring scheme can actually make
+ * a great deal of difference in the quality of the picture. Different colormaps
+ * bring out different details of the dynamics while different indexing
+ * algorithms also greatly effect what details are seen. Play around with this.
+ */
+static int
+sendpoint(double expo)
+{
+  static int index;
+  static double tmpexpo;
+
+  point.x++;
+  tmpexpo = (negative) ? expo : -1.0 * expo;
+  if (tmpexpo > 0) {
+    if (displayplanes >1) {
+	index = (int)(tmpexpo*lowrange/maxexp);
+	index = (index % lowrange) + startcolor;
+    }
+    else
+	index = 0;
+  }
+  else {
+    if (displayplanes >1) {
+	index = (int)(tmpexpo*numfreecols/minexp);
+	index = (index % numfreecols) + mincolindex;
+    }
+    else
+	index = 1;
+  }
+    BufferPoint(dpy, canvas, index, point.x, point.y);
+  if (save)
+    exponents[frame][expind[frame]++] = expo;
+  if (point.x >= width) {
+    point.y++;
+    point.x = 0;
+    if (save) {
+      b += b_inc;
+      a = min_a;
+    }
+    if (point.y >= height)
+      return FALSE;
+    else
+      return TRUE;
+  }
+  return TRUE;
+}
+
+static void
+redisplay (Window w, XExposeEvent *event)
+{
+  /*
+  * Extract the exposed area from the event and copy
+  * from the saved pixmap to the window.
+  */
+  XCopyArea(dpy, pixmap, canvas, Data_GC[0],
+	   event->x, event->y, event->width, event->height,
+	   event->x, event->y);
+}
+
+static void
+resize(void)
+{
+  Window r;
+  int n, x, y;
+  unsigned int bw, d, new_w, new_h;
+
+  XGetGeometry(dpy,canvas,&r,&x,&y,&new_w,&new_h,&bw,&d);
+  if ((new_w == width) && (new_h == height))
+    return;
+  width = new_w; height = new_h;
+  XClearWindow(dpy, canvas);
+  if (pixmap)
+    XFreePixmap(dpy, pixmap);
+  pixmap = XCreatePixmap(dpy, DefaultRootWindow(dpy),
+      width, height, DefaultDepth(dpy, screen));
+  a_inc = a_range / (double)width;
+  b_inc = b_range / (double)height;
+  point.x = -1;
+  point.y = 0;
+  run = 1;
+  a = rubber_data.p_min = min_a;
+  b = rubber_data.q_min = min_b;
+  rubber_data.p_max = max_a;
+  rubber_data.q_max = max_b;
+  freemem();
+  setupmem();
+	for (n=0;n<MAXFRAMES;n++)
+    if ((n <= maxframe) && (n != frame))
+	resized[n] = 1;
+  InitBuffer();
+  Clear();
+  Redraw();
+}
+
+static void
+redraw(double *exparray, int index, int cont)
+{
+  static int i;
+  static int x_sav, y_sav;
+
+  x_sav = point.x;
+  y_sav = point.y;
+
+  point.x = -1;
+  point.y = 0;
+
+  save=0;
+  for (i=0;i<index;i++)
+    sendpoint(exparray[i]);
+  save=1;
+
+  if (cont) {
+    point.x = x_sav;
+    point.y = y_sav;
+  }
+  else {
+    a = point.x * a_inc + min_a;
+    b = point.y * b_inc + min_b;
+  }
+  FlushBuffer();
+}
+
+static void
+Redraw(void)
+{
+  FlushBuffer();
+	point.x = -1;
+	point.y = 0;
+  run = 1;
+	a = min_a;
+	b = min_b;
+  expind[frame] = 0;
+  resized[frame] = 0;
+}
+
+/* Store color pics in PPM format and monochrome in PGM */
+static void
+save_to_file(void)
+{
+  FILE *outfile;
+  unsigned char c;
+  XImage *ximage;
+  static int i,j;
+  struct Colormap {
+    unsigned char red;
+    unsigned char green;
+    unsigned char blue;
+  };
+  struct Colormap *colormap=NULL;
+
+  if (colormap)
+    free(colormap);
+  if ((colormap=
+    (struct Colormap *)malloc(sizeof(struct Colormap)*maxcolor))
+      == NULL) {
+    fprintf(stderr,"Error malloc'ing colormap array\n");
+    exit(-1);
+  }
+  outfile = fopen(outname,"w");
+  if(!outfile) {
+    perror(outname);
+    exit(-1);
+  }
+
+  ximage=XGetImage(dpy, pixmap, 0, 0, width, height, AllPlanes, XYPixmap);
+
+  if (displayplanes > 1) {
+    for (i=0;i<maxcolor;i++) {
+      colormap[i].red=(unsigned char)(Colors[i].red >> 8);
+      colormap[i].green=(unsigned char)(Colors[i].green >> 8);
+      colormap[i].blue =(unsigned char)(Colors[i].blue >> 8);
+    }
+    fprintf(outfile,"P%d %d %d\n",6,width,height);
+  }
+  else
+    fprintf(outfile,"P%d %d %d\n",5,width,height);
+  fprintf(outfile,"# settle=%d	dwell=%d start_x=%f\n",settle,dwell,
+	start_x);
+  fprintf(outfile,"# min_a=%f  a_rng=%f	 max_a=%f\n",min_a,a_range,max_a);
+  fprintf(outfile,"# min_b=%f  b_rng=%f	 max_b=%f\n",min_b,b_range,max_b);
+  if (Rflag)
+    fprintf(outfile,"# pseudo-random forcing\n");
+  else if (force) {
+    fprintf(outfile,"# periodic forcing=");
+    for (i=0;i<maxindex;i++) {
+      fprintf(outfile,"%d",forcing[i]);
+    }
+    fprintf(outfile,"\n");
+  }
+  else
+    fprintf(outfile,"# periodic forcing=01\n");
+  if (Force) {
+    fprintf(outfile,"# function forcing=");
+    for (i=0;i<funcmaxindex;i++) {
+      fprintf(outfile,"%d",Forcing[i]);
+    }
+    fprintf(outfile,"\n");
+  }
+  fprintf(outfile,"%d\n",numcolors-1);
+
+  for (j=0;j<height;j++)
+      for (i=0;i<width;i++) {
+    c = (unsigned char)XGetPixel(ximage,i,j);
+    if (displayplanes > 1)
+	fwrite((char *)&colormap[c],sizeof colormap[0],1,outfile);
+    else
+	fwrite((char *)&c,sizeof c,1,outfile);
+      }
+  fclose(outfile);
+}
+
+static void
+recalc(void)
+{
+  static int i, x, y;
+
+  minexp = maxexp = 0.0;
+  x = y = 0;
+  for (i=0;i<expind[frame];i++) {
+    if (exponents[frame][i] < minexp)
+      minexp = exponents[frame][i];
+    if (exponents[frame][i] > maxexp)
+      maxexp = exponents[frame][i];
+  }
+}
+
+static void
+Clear(void)
+{
+      XClearWindow(dpy, canvas);
+  XCopyArea(dpy, canvas, pixmap, Data_GC[0],
+	    0, 0, width, height, 0, 0);
+  InitBuffer();
+}
+
+static void
+show_defaults(void)
+{
+
+  printf("Width=%d  Height=%d  numcolors=%d  settle=%d	dwell=%d\n",
+    width,height,numcolors,settle,dwell);
+  printf("min_a=%f  a_range=%f	max_a=%f\n", min_a,a_range,max_a);
+  printf("min_b=%f  b_range=%f	max_b=%f\n", min_b,b_range,max_b);
+  printf("minlyap=%f  minexp=%f	 maxexp=%f\n", minlyap,minexp,maxexp);
+  exit(0);
+}
+
+static void
+CreateXorGC(void)
+{
+  XGCValues values;
+
+  values.foreground = foreground;
+  values.line_style = LineSolid;
+  values.function = GXxor;
+  RubberGC = XCreateGC(dpy, DefaultRootWindow(dpy),
+	GCForeground | GCBackground | GCFunction | GCLineStyle, &values);
+}
+
+static void
+StartRubberBand(Window w, image_data_t *data, XEvent *event)
+{
+  XPoint corners[5];
+
+  nostart = 0;
+  data->rubber_band.last_x = data->rubber_band.start_x = event->xbutton.x;
+  data->rubber_band.last_y = data->rubber_band.start_y = event->xbutton.y;
+  SetupCorners(corners, data);
+  XDrawLines(dpy, canvas, RubberGC,
+      corners, sizeof(corners) / sizeof(corners[0]), CoordModeOrigin);
+}
+
+static void
+SetupCorners(XPoint *corners, image_data_t *data)
+{
+  corners[0].x = data->rubber_band.start_x;
+  corners[0].y = data->rubber_band.start_y;
+  corners[1].x = data->rubber_band.start_x;
+  corners[1].y = data->rubber_band.last_y;
+  corners[2].x = data->rubber_band.last_x;
+  corners[2].y = data->rubber_band.last_y;
+  corners[3].x = data->rubber_band.last_x;
+  corners[3].y = data->rubber_band.start_y;
+  corners[4] = corners[0];
+}
+
+static void
+TrackRubberBand(Window w, image_data_t *data, XEvent *event)
+{
+  XPoint corners[5];
+  int xdiff, ydiff;
+
+  if (nostart)
+    return;
+  SetupCorners(corners, data);
+  XDrawLines(dpy, canvas, RubberGC,
+      corners, sizeof(corners) / sizeof(corners[0]), CoordModeOrigin);
+  ydiff = event->xbutton.y - data->rubber_band.start_y;
+  xdiff = event->xbutton.x - data->rubber_band.start_x;
+  data->rubber_band.last_x = data->rubber_band.start_x + xdiff;
+  data->rubber_band.last_y = data->rubber_band.start_y + ydiff;
+  if (data->rubber_band.last_y < data->rubber_band.start_y ||
+      data->rubber_band.last_x < data->rubber_band.start_x)
+  {
+    data->rubber_band.last_y = data->rubber_band.start_y;
+    data->rubber_band.last_x = data->rubber_band.start_x;
+  }
+  SetupCorners(corners, data);
+  XDrawLines(dpy, canvas, RubberGC,
+      corners, sizeof(corners) / sizeof(corners[0]), CoordModeOrigin);
+}
+
+static void
+EndRubberBand(Window w, image_data_t *data, XEvent *event)
+{
+  XPoint corners[5];
+  XPoint top, bot;
+  double delta, diff;
+
+  nostart = 1;
+  SetupCorners(corners, data);
+  XDrawLines(dpy, canvas, RubberGC,
+      corners, sizeof(corners) / sizeof(corners[0]), CoordModeOrigin);
+  if (data->rubber_band.start_x >= data->rubber_band.last_x ||
+      data->rubber_band.start_y >= data->rubber_band.last_y)
+    return;
+  top.x = data->rubber_band.start_x;
+  bot.x = data->rubber_band.last_x;
+  top.y = data->rubber_band.start_y;
+  bot.y = data->rubber_band.last_y;
+  diff = data->q_max - data->q_min;
+  delta = (double)top.y / (double)height;
+  data->q_min += diff * delta;
+  delta = (double)(height - bot.y) / (double)height;
+  data->q_max -= diff * delta;
+  diff = data->p_max - data->p_min;
+  delta = (double)top.x / (double)width;
+  data->p_min += diff * delta;
+  delta = (double)(width - bot.x) / (double)width;
+  data->p_max -= diff * delta;
+  fflush(stdout);
+  set_new_params(w, data);
+}
+
+static void
+set_new_params(Window w, image_data_t *data)
+{
+  frame = (maxframe + 1) % MAXFRAMES;
+  if (frame > maxframe)
+    maxframe = frame;
+  a_range = data->p_max - data->p_min;
+  b_range = data->q_max - data->q_min;
+	a_minimums[frame] = min_a = data->p_min;
+	b_minimums[frame] = min_b = data->q_min;
+	a_inc = a_range / (double)width;
+	b_inc = b_range / (double)height;
+	point.x = -1;
+	point.y = 0;
+  run = 1;
+	a = min_a;
+	b = min_b;
+	a_maximums[frame] = max_a = data->p_max;
+	b_maximums[frame] = max_b = data->q_max;
+  expind[frame] = 0;;
+  Clear();
+}
+
+static void
+go_down(void)
+{
+  frame++;
+  if (frame > maxframe)
+    frame = 0;
+  jumpwin();
+}
+
+static void
+go_back(void)
+{
+  frame--;
+  if (frame < 0)
+    frame = maxframe;
+  jumpwin();
+}
+
+static void
+jumpwin(void)
+{
+  rubber_data.p_min = min_a = a_minimums[frame];
+  rubber_data.q_min = min_b = b_minimums[frame];
+  rubber_data.p_max = max_a = a_maximums[frame];
+  rubber_data.q_max = max_b = b_maximums[frame];
+  a_range = max_a - min_a;
+  b_range = max_b - min_b;
+	a_inc = a_range / (double)width;
+	b_inc = b_range / (double)height;
+	point.x = -1;
+	point.y = 0;
+	a = min_a;
+	b = min_b;
+  Clear();
+  if (resized[frame])
+    Redraw();
+  else
+    redraw(exponents[frame], expind[frame], 0);
+}
+
+static void
+go_init(void)
+{
+  frame = 0;
+  jumpwin();
+}
+
+static void
+Destroy_frame(void)
+{
+  static int i;
+
+  for (i=frame; i<maxframe; i++) {
+    exponents[frame] = exponents[frame+1];
+    expind[frame] = expind[frame+1];
+    a_minimums[frame] = a_minimums[frame+1];
+    b_minimums[frame] = b_minimums[frame+1];
+    a_maximums[frame] = a_maximums[frame+1];
+    b_maximums[frame] = b_maximums[frame+1];
+  }
+  maxframe--;
+  go_back();
+}
+
+static void
+InitBuffer(void)
+{
+  int i;
+
+  for (i = 0 ; i < maxcolor; ++i)
+    Points.npoints[i] = 0;
+}
+
+static void
+BufferPoint(Display *display, Window window, int color, int x, int y)
+{
+  if (Points.npoints[color] == MAXPOINTS)
+  {
+    XDrawPoints(display, window, Data_GC[color],
+	Points.data[color], Points.npoints[color], CoordModeOrigin);
+    XDrawPoints(display, pixmap, Data_GC[color],
+	Points.data[color], Points.npoints[color], CoordModeOrigin);
+    Points.npoints[color] = 0;
+  }
+  Points.data[color][Points.npoints[color]].x = x;
+  Points.data[color][Points.npoints[color]].y = y;
+  ++Points.npoints[color];
+}
+
+static void
+FlushBuffer(void)
+{
+  int color;
+
+  for (color = 0; color < maxcolor; ++color)
+    if (Points.npoints[color])
+    {
+	XDrawPoints(dpy, canvas, Data_GC[color],
+	  Points.data[color], Points.npoints[color],
+	  CoordModeOrigin);
+	XDrawPoints(dpy, pixmap, Data_GC[color],
+	  Points.data[color], Points.npoints[color],
+	  CoordModeOrigin);
+	Points.npoints[color] = 0;
+    }
+}
+
+static void
+print_help(void)
+{
+    printf("During run-time, interactive control can be exerted via : \n");
+    printf("Mouse buttons allow rubber-banding of a zoom box\n");
+    printf("< halves the 'dwell', > doubles the 'dwell'\n");
+    printf("[ halves the 'settle', ] doubles the 'settle'\n");
+    printf("D flushes the drawing buffer\n");
+    printf("e or E recalculates color indices\n");
+    printf("f or F saves exponents to a file\n");
+    printf("h or H or ? displays this message\n");
+    printf("i decrements, I increments the stripe interval\n");
+    printf("KJMN increase/decrease minimum negative exponent\n");
+    printf("m increments the map index, changing maps\n");
+    printf("p or P reverses the colormap for negative/positive exponents\n");
+    printf("r redraws without recalculating\n");
+    printf("R redraws, recalculating with new dwell and settle values\n");
+    printf("s or S spins the colorwheel\n");
+    printf("u pops back up to the last zoom\n");
+    printf("U pops back up to the first picture\n");
+    printf("v or V displays the values of various settings\n");
+    printf("w decrements, W increments the color wheel index\n");
+    printf("x or X clears the window\n");
+    printf("q or Q exits\n");
+}
+
+static void
+print_values(void)
+{
+    static int i;
+
+    printf("\nminlyap=%f minexp=%f maxexp=%f\n",minlyap,minexp,maxexp);
+    printf("width=%d height=%d\n",width,height);
+    printf("settle=%d  dwell=%d start_x=%f\n",settle,dwell, start_x);
+    printf("min_a=%f  a_rng=%f	max_a=%f\n",min_a,a_range,max_a);
+    printf("min_b=%f  b_rng=%f	max_b=%f\n",min_b,b_range,max_b);
+    if (Rflag)
+  printf("pseudo-random forcing\n");
+    else if (force) {
+  printf("periodic forcing=");
+  for (i=0;i<maxindex;i++)
+    printf("%d",forcing[i]);
+  printf("\n");
+    }
+    else
+  printf("periodic forcing=01\n");
+    if (Force) {
+  printf("function forcing=");
+  for (i=0;i<funcmaxindex;i++) {
+    printf("%d",Forcing[i]);
+  }
+  printf("\n");
+    }
+    printf("numcolors=%d\n",numcolors-1);
+}
+
+static void
+freemem(void)
+{
+  static int i;
+
+	for (i=0;i<MAXFRAMES;i++)
+		free(exponents[i]);
+}
+
+static void
+setupmem(void)
+{
+  static int i;
+
+	for (i=0;i<MAXFRAMES;i++) {
+		if((exponents[i]=
+		    (double *)malloc(sizeof(double)*width*height))==NULL){
+		    fprintf(stderr,"Error malloc'ing exponent array.\n");
+		    exit(-1);
+		}
+	}
+}
+
+static void
+setforcing(void)
+{
+  static int i;
+  for (i=0;i<MAXINDEX;i++)
+    forcing[i] = (ya_random() > prob) ? 0 : 1;
+}