--- /dev/null
+/* 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;
+}
projects / xscreensaver / blobdiff