1 /* Lyap - calculate and display Lyapunov exponents */
3 /* Written by Ron Record (rr@sco) 03 Sep 1991 */
5 /* The idea here is to calculate the Lyapunov exponent for a periodically
6 * forced logistic map (later i added several other nonlinear maps of the unit
7 * interval). In order to turn the 1-dimensional parameter space of the
8 * logistic map into a 2-dimensional parameter space, select two parameter
9 * values ('a' and 'b') then alternate the iterations of the logistic map using
10 * first 'a' then 'b' as the parameter. This program accepts an argument to
11 * specify a forcing function, so instead of just alternating 'a' and 'b', you
12 * can use 'a' as the parameter for say 6 iterations, then 'b' for 6 iterations
13 * and so on. An interesting forcing function to look at is abbabaab (the
14 * Morse-Thue sequence, an aperiodic self-similar, self-generating sequence).
15 * Anyway, step through all the values of 'a' and 'b' in the ranges you want,
16 * calculating the Lyapunov exponent for each pair of values. The exponent
17 * is calculated by iterating out a ways (specified by the variable "settle")
18 * then on subsequent iterations calculating an average of the logarithm of
19 * the absolute value of the derivative at that point. Points in parameter
20 * space with a negative Lyapunov exponent are colored one way (using the
21 * value of the exponent to index into a color map) while points with a
22 * non-negative exponent are colored differently.
24 * The algorithm was taken from the September 1991 Scientific American article
25 * by A. K. Dewdney who gives credit to Mario Markus of the Max Planck Institute
26 * for its creation. Additional information and ideas were gleaned from the
27 * discussion on alt.fractals involving Stephen Hall, Ed Kubaitis, Dave Platt
28 * and Baback Moghaddam. Assistance with colormaps and spinning color wheels
29 * and X was gleaned from Hiram Clawson. Rubber banding code was adapted from
30 * an existing Mandelbrot program written by Stacey Campbell.
33 #define LYAP_PATCHLEVEL 4
34 #define LYAP_VERSION "#(@) lyap 2.3 2/20/92"
39 #include "screenhack.h"
44 #include <X11/cursorfont.h>
45 #include <X11/Xutil.h>
47 char *progclass = "XLyap";
58 "*colorExponent: 1.0",
60 "*randomForce: ", /* 0.5 */
65 "*function: 10101010",
66 "*forcingFunction: abbabaab",
67 "*bRange: ", /* 2.0 */
69 "*mapIndex: ", /* 0 */
75 "*aRange: ", /* 2.0 */
79 XrmOptionDescRec options [] = {
80 { "-randomize", ".randomize", XrmoptionNoArg, "true" },
81 { "-builtin", ".builtin", XrmoptionSepArg, 0 },
82 { "-C", ".minColor", XrmoptionSepArg, 0 }, /* n */
83 { "-D", ".dwell", XrmoptionSepArg, 0 }, /* n */
84 { "-L", ".useLog", XrmoptionNoArg, "true" },
85 { "-M", ".colorExponent", XrmoptionSepArg, 0 }, /* r */
86 { "-O", ".colorOffset", XrmoptionSepArg, 0 }, /* n */
87 { "-R", ".randomForce", XrmoptionSepArg, 0 }, /* p */
88 { "-S", ".settle", XrmoptionSepArg, 0 }, /* n */
89 { "-a", ".minA", XrmoptionSepArg, 0 }, /* r */
90 { "-b", ".minB", XrmoptionSepArg, 0 }, /* n */
91 { "-c", ".wheels", XrmoptionSepArg, 0 }, /* n */
92 { "-F", ".function", XrmoptionSepArg, 0 }, /* 10101010 */
93 { "-f", ".forcingFunction", XrmoptionSepArg, 0 }, /* abbabaab */
94 { "-h", ".bRange", XrmoptionSepArg, 0 }, /* r */
95 { "-i", ".startX", XrmoptionSepArg, 0 }, /* r */
96 { "-m", ".mapIndex", XrmoptionSepArg, 0 }, /* n */
97 { "-o", ".outputFile", XrmoptionSepArg, 0 }, /* filename */
98 { "-p", ".beNegative", XrmoptionNoArg, "true" },
99 { "-r", ".rgbMax", XrmoptionSepArg, 0 }, /* n */
100 { "-s", ".spinLength", XrmoptionSepArg, 0 }, /* n */
101 { "-v", ".show", XrmoptionNoArg, "true" },
102 { "-w", ".aRange", XrmoptionSepArg, 0 }, /* r */
107 #define ABS(a) (((a)<0) ? (0-(a)) : (a) )
108 #define Min(x,y) ((x < y)?x:y)
109 #define Max(x,y) ((x > y)?x:y)
111 #ifdef SIXTEEN_COLORS
112 #define MAXPOINTS 128
119 static int maxcolor=16, startcolor=0, color_offset=0, mincolindex=1;
120 static int dwell=50, settle=25;
121 static int width=128, height=128, xposition=128, yposition=128;
123 #define MAXPOINTS 256
130 static int maxcolor=256, startcolor=17, color_offset=96, mincolindex=33;
131 static int dwell=100, settle=50;
132 static int width=256, height=256;
142 static Visual *visual;
144 static unsigned long foreground, background;
146 static Window canvas;
153 int start_x, start_y;
155 } rubber_band_data_t;
159 double p_min, p_max, q_min, q_max;
160 rubber_band_data_t rubber_band;
163 typedef struct points_t {
164 XPoint data[MAXCOLOR][MAXPOINTS];
165 int npoints[MAXCOLOR];
168 static points_t Points;
169 static image_data_t rubber_data;
176 static GC Data_GC[MAXCOLOR], RubberGC;
179 #define FUNCMAXINDEX 16
183 typedef double (*PFD)(double,double);
185 static double logistic(double,double), circle(double,double), leftlog(double,double), rightlog(double,double), doublelog(double,double);
186 static double dlogistic(double,double), dcircle(double,double), dleftlog(double,double), drightlog(double,double), ddoublelog(double,double);
187 static PFD map, deriv;
188 static PFD Maps[NUMMAPS] = { logistic, circle, leftlog, rightlog, doublelog };
189 static PFD Derivs[NUMMAPS] = { dlogistic, dcircle, dleftlog, drightlog, ddoublelog };
191 static int aflag=0, bflag=0, wflag=0, hflag=0, Rflag=0;
192 static double pmins[NUMMAPS] = { 2.0, 0.0, 0.0, 0.0, 0.0 };
193 static double pmaxs[NUMMAPS] = { 4.0, 1.0, 6.75, 6.75, 16.0 };
194 static double amins[NUMMAPS] = { 2.0, 0.0, 0.0, 0.0, 0.0 };
195 static double aranges[NUMMAPS] = { 2.0, 1.0, 6.75, 6.75, 16.0 };
196 static double bmins[NUMMAPS] = { 2.0, 0.0, 0.0, 0.0, 0.0 };
197 static double branges[NUMMAPS] = { 2.0, 1.0, 6.75, 6.75, 16.0 };
199 static int forcing[MAXINDEX] = { 0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,
200 0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,
201 0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1 };
202 static int Forcing[FUNCMAXINDEX] = { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 };
204 static int maxindex = MAXINDEX;
205 static int funcmaxindex = FUNCMAXINDEX;
206 static double min_a=2.0, min_b=2.0, a_range=2.0, b_range=2.0, minlyap=1.0;
207 static double max_a=4.0, max_b=4.0;
208 static double start_x=0.65, lyapunov, a_inc, b_inc, a, b;
209 static int numcolors=16, numfreecols, displayplanes, lowrange;
211 static Pixmap pixmap;
212 static Colormap cmap;
213 static XColor Colors[MAXCOLOR];
214 static double *exponents[MAXFRAMES];
215 static double a_minimums[MAXFRAMES], b_minimums[MAXFRAMES];
216 static double a_maximums[MAXFRAMES], b_maximums[MAXFRAMES];
217 static double minexp, maxexp, prob=0.5;
218 static int expind[MAXFRAMES]={0}, resized[MAXFRAMES]={0};
219 static int numwheels=MAXWHEELS, force=0, Force=0, negative=1;
220 static int rgb_max=65000, nostart=1, stripe_interval=7;
221 static int save=1, show=0, useprod=1, spinlength=256, savefile=0;
222 static int maxframe=0, frame=0, dorecalc=0, mapindex=0, run=1;
223 static char *outname="lyap.out";
226 const char * const version = LYAP_VERSION;
228 static void resize(void);
229 static void redisplay(Window w, XExposeEvent *event);
230 static void Spin(Window w);
231 static void show_defaults(void);
232 static void StartRubberBand(Window w, image_data_t *data, XEvent *event);
233 static void TrackRubberBand(Window w, image_data_t *data, XEvent *event);
234 static void EndRubberBand(Window w, image_data_t *data, XEvent *event);
235 static void CreateXorGC(void);
236 static void InitBuffer(void);
237 static void BufferPoint(Display *display, Window window, int color,
239 static void FlushBuffer(void);
240 static void init_canvas(void);
241 static void init_data(void);
242 static void init_color(void);
243 static void parseargs(void);
244 static void Clear(void);
245 static void setupmem(void);
246 static void main_event(void);
247 static int complyap(void);
248 static void Getkey(XKeyEvent *event);
249 static int sendpoint(double expo);
250 static void save_to_file(void);
251 static void setforcing(void);
252 static void check_params(int mapnum, int parnum);
253 static void usage(void);
254 static void Destroy_frame(void);
255 static void freemem(void);
256 static void Redraw(void);
257 static void redraw(double *exparray, int index, int cont);
258 static void recalc(void);
259 static void SetupCorners(XPoint *corners, image_data_t *data);
260 static void set_new_params(Window w, image_data_t *data);
261 static void go_down(void);
262 static void go_back(void);
263 static void go_init(void);
264 static void jumpwin(void);
265 static void print_help(void);
266 static void print_values(void);
270 screenhack (Display *d, Window window)
272 XWindowAttributes xgwa;
275 XGetWindowAttributes (dpy, window, &xgwa);
277 height = xgwa.height;
278 visual = xgwa.visual;
279 cmap = xgwa.colormap;
283 if (get_boolean_resource("randomize", "Boolean"))
284 builtin = random() % 22;
286 char *s = get_string_resource("builtin", "Integer");
297 min_a = 3.75; aflag++;
298 min_b = 3.299999; bflag++;
299 a_range = 0.05; wflag++;
300 b_range = 0.05; hflag++;
307 min_a = 3.8; aflag++;
308 min_b = 3.2; bflag++;
309 b_range = .05; hflag++;
310 a_range = .05; wflag++;
315 min_a = 3.4; aflag++;
316 min_b = 3.04; bflag++;
317 a_range = .5; wflag++;
318 b_range = .5; hflag++;
325 min_a = 3.5; aflag++;
326 min_b = 3.0; bflag++;
327 a_range = 0.2; wflag++;
328 b_range = 0.2; hflag++;
335 min_a = 3.55667; aflag++;
336 min_b = 3.2; bflag++;
337 b_range = .05; hflag++;
338 a_range = .05; wflag++;
343 min_a = 3.79; aflag++;
344 min_b = 3.22; bflag++;
345 b_range = .02999; hflag++;
346 a_range = .02999; wflag++;
351 min_a = 3.7999; aflag++;
352 min_b = 3.299999; bflag++;
353 a_range = 0.2; wflag++;
354 b_range = 0.2; hflag++;
361 min_a = 3.89; aflag++;
362 min_b = 3.22; bflag++;
363 b_range = .028; hflag++;
364 a_range = .02999; wflag++;
371 min_a = 3.2; aflag++;
372 min_b = 3.7; bflag++;
373 a_range = 0.05; wflag++;
374 b_range = .005; hflag++;
383 minlyap = maxexp = ABS(-0.85);
384 minexp = -1.0 * minlyap;
392 minlyap = maxexp = ABS(-0.85);
393 minexp = -1.0 * minlyap;
400 minlyap = maxexp = ABS(-0.85);
401 minexp = -1.0 * minlyap;
409 minlyap = maxexp = ABS(-0.85);
410 minexp = -1.0 * minlyap;
418 minlyap = maxexp = ABS(-0.85);
419 minexp = -1.0 * minlyap;
426 minlyap = maxexp = ABS(-0.85);
427 minexp = -1.0 * minlyap;
429 min_a = 3.91; aflag++;
430 a_range = 0.0899999999; wflag++;
431 min_b = 3.28; bflag++;
432 b_range = 0.35; hflag++;
439 minlyap = maxexp = ABS(-0.85);
440 minexp = -1.0 * minlyap;
446 minlyap = maxexp = ABS(-0.85);
447 minexp = -1.0 * minlyap;
454 minlyap = maxexp = ABS(-0.85);
455 minexp = -1.0 * minlyap;
462 minlyap = maxexp = ABS(-0.85);
463 minexp = -1.0 * minlyap;
471 minlyap = maxexp = ABS(-0.85);
472 minexp = -1.0 * minlyap;
479 minlyap = maxexp = ABS(-0.85);
480 minexp = -1.0 * minlyap;
488 minlyap = maxexp = ABS(-0.85);
489 minexp = -1.0 * minlyap;
497 minlyap = maxexp = ABS(-0.85);
498 minexp = -1.0 * minlyap;
505 maxindex = strlen(ff);
506 if (maxindex > MAXINDEX)
510 while (bindex < maxindex) {
512 forcing[bindex++] = 0;
514 forcing[bindex++] = 1;
522 screen = DefaultScreen(dpy);
523 background = BlackPixel(dpy, screen);
526 if (displayplanes > 1)
527 foreground = startcolor;
529 foreground = WhitePixel(dpy, screen);
532 * Create the window to display the Lyapunov exponents
537 if (window != DefaultRootWindow(dpy))
538 XSelectInput(dpy,canvas,KeyPressMask|ButtonPressMask|ButtonMotionMask|
539 ButtonReleaseMask|ExposureMask|StructureNotifyMask);
540 if (displayplanes > 1) {
543 XQueryColors(dpy, DefaultColormap(dpy, DefaultScreen(dpy)),
546 pixmap = XCreatePixmap(dpy, DefaultRootWindow(dpy),
547 width, height, DefaultDepth(dpy, screen));
548 rubber_data.band_cursor = XCreateFontCursor(dpy, XC_hand2);
561 if (complyap() == TRUE)
563 n = XEventsQueued(dpy, QueuedAfterFlush);
565 XNextEvent(dpy, &event);
572 redisplay(canvas, &event.xexpose);
574 case ConfigureNotify:
578 StartRubberBand(canvas, &rubber_data, &event);
581 TrackRubberBand(canvas, &rubber_data, &event);
584 EndRubberBand(canvas, &rubber_data, &event);
590 /* complyap() is the guts of the program. This is where the Lyapunov exponent
591 * is calculated. For each iteration (past some large number of iterations)
592 * calculate the logarithm of the absolute value of the derivative at that
593 * point. Then average them over some large number of iterations. Some small
594 * speed up is achieved by utilizing the fact that log(a*b) = log(a) + log(b).
600 double total, prod, x, r;
606 if (sendpoint(lyapunov) == TRUE)
624 r = (forcing[bindex]) ? b : a;
627 map = Maps[Forcing[findex]];
629 for (i=0;i<settle;i++) { /* Here's where we let the thing */
630 x = (*map)(x, r); /* "settle down". There is usually */
631 if (++bindex >= maxindex) { /* some initial "noise" in the */
632 bindex = 0; /* iterations. How can we optimize */
633 if (Rflag) /* the value of settle ??? */
636 r = (forcing[bindex]) ? b : a;
638 if (++findex >= funcmaxindex)
640 map = Maps[Forcing[findex]];
644 deriv = Derivs[Forcing[findex]];
646 if (useprod) { /* using log(a*b) */
647 for (i=0;i<dwell;i++) {
649 prod *= ABS((*deriv)(x, r));
650 /* we need to prevent overflow and underflow */
651 if ((prod > 1.0e12) || (prod < 1.0e-12)) {
655 if (++bindex >= maxindex) {
660 r = (forcing[bindex]) ? b : a;
662 if (++findex >= funcmaxindex)
664 map = Maps[Forcing[findex]];
665 deriv = Derivs[Forcing[findex]];
669 lyapunov = (total * M_LOG2E) / (double)dwell;
671 else { /* use log(a) + log(b) */
672 for (i=0;i<dwell;i++) {
674 total += log(ABS((*deriv)(x, r)));
675 if (++bindex >= maxindex) {
680 r = (forcing[bindex]) ? b : a;
682 if (++findex >= funcmaxindex)
684 map = Maps[Forcing[findex]];
685 deriv = Derivs[Forcing[findex]];
688 lyapunov = (total * M_LOG2E) / (double)dwell;
690 if (sendpoint(lyapunov) == TRUE)
701 logistic(double x, double r) /* the familiar logistic map */
703 return(r * x * (1.0 - x));
707 dlogistic(double x, double r) /* the derivative of logistic map */
709 return(r - (2.0 * r * x));
713 circle(double x, double r) /* sin() hump or sorta like the circle map */
715 return(r * sin(M_PI * x));
719 dcircle(double x, double r) /* derivative of the "sin() hump" */
721 return(r * M_PI * cos(M_PI * x));
725 leftlog(double x, double r) /* left skewed logistic */
730 return(r * x * d * d);
734 dleftlog(double x, double r) /* derivative of the left skewed logistic */
736 return(r * (1.0 - (4.0 * x) + (3.0 * x * x)));
740 rightlog(double x, double r) /* right skewed logistic */
742 return(r * x * x * (1.0 - x));
746 drightlog(double x, double r) /* derivative of the right skewed logistic */
748 return(r * ((2.0 * x) - (3.0 * x * x)));
752 doublelog(double x, double r) /* double logistic */
757 return(r * x * x * d * d);
761 ddoublelog(double x, double r) /* derivative of the double logistic */
766 return(r * ((2.0 * x) - (6.0 * d) + (4.0 * x * d)));
772 numcolors = XDisplayCells(dpy, XDefaultScreen(dpy));
773 displayplanes = DisplayPlanes(dpy, XDefaultScreen(dpy));
774 if (numcolors > maxcolor)
775 numcolors = maxcolor;
776 numfreecols = numcolors - mincolindex;
777 lowrange = mincolindex - startcolor;
778 a_inc = a_range / (double)width;
779 b_inc = b_range / (double)height;
782 a = rubber_data.p_min = min_a;
783 b = rubber_data.q_min = min_b;
784 rubber_data.p_max = max_a;
785 rubber_data.q_max = max_b;
797 * create default, writable, graphics contexts for the canvas.
799 for (i=0; i<maxcolor; i++) {
800 Data_GC[i] = XCreateGC(dpy, DefaultRootWindow(dpy),
801 (unsigned long) NULL, (XGCValues *) NULL);
802 /* set the background to black */
803 XSetBackground(dpy,Data_GC[i],BlackPixel(dpy,XDefaultScreen(dpy)));
804 /* set the foreground of the ith context to i */
805 XSetForeground(dpy, Data_GC[i], i);
807 if (displayplanes == 1) {
808 XSetForeground(dpy,Data_GC[0],BlackPixel(dpy,XDefaultScreen(dpy)));
809 XSetForeground(dpy,Data_GC[1],WhitePixel(dpy,XDefaultScreen(dpy)));
815 hls2rgb(int hue_light_sat[3],
816 int rgb[3]) /* Each in range [0..65535] */
818 unsigned short r, g, b;
819 hsv_to_rgb((int) (hue_light_sat[0] / 10), /* 0-3600 -> 0-360 */
820 (int) ((hue_light_sat[2]/1000.0) * 64435), /* 0-1000 -> 0-65535 */
821 (int) ((hue_light_sat[1]/1000.0) * 64435), /* 0-1000 -> 0-65535 */
837 int ncolors = maxcolor;
838 Bool writable = False;
839 make_smooth_colormap(dpy, visual, cmap,
840 colors, &ncolors, True, &writable, True);
842 for (i = 0; i < maxcolor; i++)
843 XSetForeground(dpy, Data_GC[i],
844 colors[((int) ((i / ((float)maxcolor)) * ncolors))].pixel);
847 static int i, j, colgap, leg, step;
848 static Visual *visual;
852 def_cmap = DefaultColormap(dpy, DefaultScreen(dpy));
853 for (i=0; i<numcolors; i++) {
855 Colors[i].flags = DoRed|DoGreen|DoBlue;
858 /* Try to write into a new color map */
859 visual = DefaultVisual(dpy, DefaultScreen(dpy));
860 cmap = XCreateColormap(dpy, canvas, visual, AllocAll);
861 XQueryColors(dpy, def_cmap, Colors, numcolors);
863 colgap = rgb_max / mincolindex;
866 hls[0] = 50; /* Hue in low range */
867 hls[2] = 1000; /* Fully saturated */
868 for (i=startcolor; i<lowrange + startcolor; i++) {
869 hls[1] = 1000L * (i-startcolor) / lowrange;
871 Colors[i].red = rgb[0];
872 Colors[i].green = rgb[1];
873 Colors[i].blue = rgb[2];
875 colgap = rgb_max / numcolors;
877 XQueryColors(dpy, def_cmap, Colors, numcolors);
878 else if (numwheels == 1) {
879 colgap = 2*rgb_max/(numcolors - color_offset);
880 for (i=mincolindex; i<(numcolors/2); i++) {
882 Colors[i].green=((i+color_offset)*colgap);
883 Colors[i].red=((i+color_offset)*colgap);
885 for (i=(numcolors/2); i<(numcolors); i++) {
887 Colors[i].green=(((numcolors-i)+color_offset)*colgap);
888 Colors[i].red=(((numcolors-i)+color_offset)*colgap);
891 else if (numwheels == 2) {
892 hls[0] = 800; /* Hue in mid range */
893 hls[2] = 1000; /* Fully saturated */
894 for (i=startcolor; i<lowrange + startcolor; i++) {
895 hls[1] = 1000L * (i-startcolor) / lowrange;
897 Colors[i].red = rgb[0];
898 Colors[i].green = rgb[1];
899 Colors[i].blue = rgb[2];
901 for (i=mincolindex; i<(numcolors/2); i++) {
902 Colors[i].blue = rgb_max;
904 Colors[i].red=(i*2*rgb_max/numcolors);
906 for (i=(numcolors/2); i<numcolors; i++) {
907 Colors[i].blue = rgb_max;
909 Colors[i].red=((numcolors - i)*2*rgb_max/numcolors);
912 else if (numwheels == 3) {
913 hls[0] = 800; /* Hue in mid range */
914 hls[2] = 1000; /* Fully saturated */
915 for (i=startcolor; i<lowrange + startcolor; i++) {
916 hls[1] = 1000L * (i-startcolor) / lowrange;
918 Colors[i].red = rgb[0];
919 Colors[i].green = rgb[1];
920 Colors[i].blue = rgb[2];
922 colgap = 4*rgb_max/numcolors;
923 for (i=mincolindex; i<(numcolors/4); i++) {
924 Colors[i].blue = rgb_max;
926 Colors[i].red=(i*colgap);
928 for (i=(numcolors/4); i<(numcolors/2); i++) {
929 Colors[i].red = rgb_max;
931 Colors[i].blue=((numcolors/2) - i) * colgap;
933 for (i=(numcolors/2); i<(0.75*numcolors); i++) {
934 Colors[i].red = rgb_max;
935 Colors[i].blue=(i * colgap);
938 for (i=(0.75*numcolors); i<numcolors; i++) {
939 Colors[i].blue = rgb_max;
941 Colors[i].red=(numcolors-i)*colgap;
944 else if (numwheels == 4) {
945 hls[0] = 800; /* Hue in mid range */
946 hls[2] = 1000; /* Fully saturated */
947 for (i=startcolor; i<lowrange + startcolor; i++) {
948 hls[1] = 1000L * (i-startcolor) / lowrange;
950 Colors[i].red = rgb[0];
951 Colors[i].green = rgb[1];
952 Colors[i].blue = rgb[2];
954 colgap = numwheels * rgb_max / numcolors;
955 for (i=mincolindex; i<(numcolors/numwheels); i++) {
956 Colors[i].blue = rgb_max;
958 Colors[i].red=(i*colgap);
960 for (i=(numcolors/numwheels); i<(2*numcolors/numwheels); i++) {
961 Colors[i].red = rgb_max;
963 Colors[i].blue=((2*numcolors/numwheels) - i) * colgap;
965 for (i=(2*numcolors/numwheels); i<numcolors; i++) {
966 Colors[i].red = rgb_max;
967 Colors[i].green=(i - (2*numcolors/numwheels)) * colgap;
971 else if (numwheels == 5) {
972 hls[1] = 700; /* Lightness in midrange */
973 hls[2] = 1000; /* Fully saturated */
974 for (i=mincolindex; i<numcolors; i++) {
975 hls[0] = 3600L * i / numcolors;
977 Colors[i].red = rgb[0];
978 Colors[i].green = rgb[1];
979 Colors[i].blue = rgb[2];
981 for (i=mincolindex; i<numcolors; i+=stripe_interval) {
982 hls[0] = 3600L * i / numcolors;
984 Colors[i].red = rgb[0] / 2;
985 Colors[i].green = rgb[1] / 2;
986 Colors[i].blue = rgb[2] / 2;
989 else if (numwheels == 6) {
990 hls[0] = 800; /* Hue in mid range */
991 hls[2] = 1000; /* Fully saturated */
992 for (i=startcolor; i<lowrange + startcolor; i++) {
993 hls[1] = 1000L * (i-startcolor) / lowrange;
995 Colors[i].red = rgb[0];
996 Colors[i].green = rgb[1];
997 Colors[i].blue = rgb[2];
999 step = numfreecols / 3;
1000 leg = step+mincolindex;
1001 for (i = mincolindex; i < leg; ++i)
1003 Colors[i].pixel = i;
1004 Colors[i].red = fabs(65535 - (double)i / step * 65535.0);
1005 Colors[i].blue = (double)i / step * 65535.0;
1006 Colors[i].green = 0;
1007 Colors[i].flags = DoRed | DoGreen | DoBlue;
1009 for (j = 0, i = leg, leg += step; i < leg; ++i, ++j)
1011 Colors[i].pixel = i;
1012 Colors[i].red = (double)j / step * 65535.0;
1013 Colors[i].blue = 65535;
1014 Colors[i].green = Colors[i].red;
1015 Colors[i].flags = DoRed | DoGreen | DoBlue;
1017 for (j = 0, i = leg, leg += step; i < leg; ++i, ++j)
1019 Colors[i].pixel = i;
1020 Colors[i].red = 65535;
1021 Colors[i].blue = fabs(65535 - (double)j / step * 65535.0);
1022 Colors[i].green = Colors[i].blue;
1023 Colors[i].flags = DoRed | DoGreen | DoBlue;
1026 else if (numwheels == MAXWHEELS) { /* rainbow palette */
1027 hls[1] = 500; /* Lightness in midrange */
1028 hls[2] = 1000; /* Fully saturated */
1029 for (i=mincolindex; i<numcolors; i++) {
1030 hls[0] = 3600L * i / numcolors;
1032 Colors[i].red = rgb[0];
1033 Colors[i].green = rgb[1];
1034 Colors[i].blue = rgb[2];
1037 XStoreColors(dpy, cmap, Colors, numcolors);
1039 XSetWindowColormap(dpy, canvas, cmap);
1047 int bindex=0, findex;
1052 maxexp=minlyap; minexp= -1.0 * minlyap;
1054 mincolindex = get_integer_resource("minColor", "Integer");
1055 dwell = get_integer_resource("dwell", "Integer");
1058 char *optarg = get_string_resource("function", "String");
1059 funcmaxindex = strlen(optarg);
1060 if (funcmaxindex > FUNCMAXINDEX)
1064 for (findex=0;findex<funcmaxindex;findex++) {
1065 Forcing[findex] = (int)(*ch++ - '0');;
1066 if (Forcing[findex] >= NUMMAPS)
1071 if (get_boolean_resource("useLog", "Boolean"))
1074 minlyap=ABS(get_float_resource("colorExponent", "Float"));
1076 minexp= -1.0 * minlyap;
1078 color_offset = get_integer_resource("colorOffset", "Integer");
1080 maxcolor=ABS(get_integer_resource("maxColor", "Integer"));
1081 if ((maxcolor - startcolor) <= 0)
1083 if ((maxcolor - mincolindex) <= 0) {
1088 s = get_string_resource("randomForce", "Float");
1090 prob=atof(s); Rflag++; setforcing();
1093 settle = get_integer_resource("settle", "Integer");
1095 s = get_string_resource("minA", "Float");
1101 s = get_string_resource("minB", "Float");
1103 min_b=atof(s); bflag++;
1106 numwheels = get_integer_resource("wheels", "Integer");
1108 s = get_string_resource("forcingFunction", "String");
1110 maxindex = strlen(s);
1111 if (maxindex > MAXINDEX)
1115 while (bindex < maxindex) {
1117 forcing[bindex++] = 0;
1118 else if (*ch == 'b')
1119 forcing[bindex++] = 1;
1126 s = get_string_resource("bRange", "Float");
1132 start_x = get_float_resource("startX", "Float");
1134 s = get_string_resource("mapIndex", "Integer");
1137 if ((mapindex >= NUMMAPS) || (mapindex < 0))
1139 map = Maps[mapindex];
1140 deriv = Derivs[mapindex];
1142 min_a = amins[mapindex];
1144 a_range = aranges[mapindex];
1146 min_b = bmins[mapindex];
1148 b_range = branges[mapindex];
1150 for (i=0;i<FUNCMAXINDEX;i++)
1151 Forcing[i] = mapindex;
1154 outname = get_string_resource("outputFile", "Integer");
1156 if (get_boolean_resource("beNegative", "Boolean"))
1159 rgb_max = get_integer_resource("rgbMax", "Integer");
1160 spinlength = get_integer_resource("spinLength", "Integer");
1161 show = get_boolean_resource("show", "Boolean");
1163 s = get_string_resource("aRange", "Float");
1165 a_range = atof(s); wflag++;
1168 max_a = min_a + a_range;
1169 max_b = min_b + b_range;
1171 a_minimums[0] = min_a; b_minimums[0] = min_b;
1172 a_maximums[0] = max_a; b_maximums[0] = max_b;
1175 if (maxindex == funcmaxindex)
1176 for (findex=0;findex<funcmaxindex;findex++)
1177 check_params(Forcing[findex],forcing[findex]);
1179 fprintf(stderr, "Warning! Unable to check parameters\n");
1181 check_params(mapindex,2);
1185 check_params(int mapnum, int parnum)
1189 if ((max_a > pmaxs[mapnum]) || (min_a < pmins[mapnum])) {
1190 fprintf(stderr, "Warning! Parameter 'a' out of range.\n");
1191 fprintf(stderr, "You have requested a range of (%f,%f).\n",
1193 fprintf(stderr, "Valid range is (%f,%f).\n",
1194 pmins[mapnum],pmaxs[mapnum]);
1198 if ((max_b > pmaxs[mapnum]) || (min_b < pmins[mapnum])) {
1199 fprintf(stderr, "Warning! Parameter 'b' out of range.\n");
1200 fprintf(stderr, "You have requested a range of (%f,%f).\n",
1202 fprintf(stderr, "Valid range is (%f,%f).\n",
1203 pmins[mapnum],pmaxs[mapnum]);
1211 fprintf(stderr,"lyap [-BLs][-W#][-H#][-a#][-b#][-w#][-h#][-x xstart]\n");
1212 fprintf(stderr,"\t[-M#][-S#][-D#][-f string][-r#][-O#][-C#][-c#][-m#]\n");
1214 fprintf(stderr,"\t[-F string]\n");
1216 fprintf(stderr,"\tWhere: -C# specifies the minimum color index\n");
1217 fprintf(stderr,"\t -r# specifies the maxzimum rgb value\n");
1218 fprintf(stderr,"\t -u displays this message\n");
1219 fprintf(stderr,"\t -a# specifies the minimum horizontal parameter\n");
1220 fprintf(stderr,"\t -b# specifies the minimum vertical parameter\n");
1221 fprintf(stderr,"\t -w# specifies the horizontal parameter range\n");
1222 fprintf(stderr,"\t -h# specifies the vertical parameter range\n");
1223 fprintf(stderr,"\t -D# specifies the dwell\n");
1224 fprintf(stderr,"\t -S# specifies the settle\n");
1225 fprintf(stderr,"\t -H# specifies the initial window height\n");
1226 fprintf(stderr,"\t -W# specifies the initial window width\n");
1227 fprintf(stderr,"\t -O# specifies the color offset\n");
1228 fprintf(stderr,"\t -c# specifies the desired color wheel\n");
1229 fprintf(stderr,"\t -m# specifies the desired map (0-4)\n");
1230 fprintf(stderr,"\t -f aabbb specifies a forcing function of 00111\n");
1232 fprintf(stderr,"\t -F 00111 specifies the function forcing function\n");
1234 fprintf(stderr,"\t -L indicates use log(x)+log(y) rather than log(xy)\n");
1235 fprintf(stderr,"\tDuring display :\n");
1236 fprintf(stderr,"\t Use the mouse to zoom in on an area\n");
1237 fprintf(stderr,"\t e or E recalculates color indices\n");
1238 fprintf(stderr,"\t f or F saves exponents to a file\n");
1239 fprintf(stderr,"\t KJmn increase/decrease minimum negative exponent\n");
1240 fprintf(stderr,"\t r or R redraws\n");
1241 fprintf(stderr,"\t s or S spins the colorwheel\n");
1242 fprintf(stderr,"\t w or W changes the color wheel\n");
1243 fprintf(stderr,"\t x or X clears the window\n");
1244 fprintf(stderr,"\t q or Q exits\n");
1252 for (i=0;i<=maxframe;i++)
1253 redraw(exponents[i], expind[i], 1);
1262 if (displayplanes > 1) {
1263 for (j=0;j<spinlength;j++) {
1264 tmpxcolor = Colors[mincolindex].pixel;
1265 for (i=mincolindex;i<numcolors-1;i++)
1266 Colors[i].pixel = Colors[i+1].pixel;
1267 Colors[numcolors-1].pixel = tmpxcolor;
1268 XStoreColors(dpy, cmap, Colors, numcolors);
1270 for (j=0;j<spinlength;j++) {
1271 tmpxcolor = Colors[numcolors-1].pixel;
1272 for (i=numcolors-1;i>mincolindex;i--)
1273 Colors[i].pixel = Colors[i-1].pixel;
1274 Colors[mincolindex].pixel = tmpxcolor;
1275 XStoreColors(dpy, cmap, Colors, numcolors);
1281 Getkey(XKeyEvent *event)
1285 if (XLookupString(event, (char *)&key, sizeof(key), (KeySym *)0,
1286 (XComposeStatus *) 0) > 0)
1288 case '<': dwell /= 2; if (dwell < 1) dwell = 1; break;
1289 case '>': dwell *= 2; break;
1290 case '[': settle /= 2; if (settle < 1) settle = 1; break;
1291 case ']': settle *= 2; break;
1292 case 'd': go_down(); break;
1293 case 'D': FlushBuffer(); break;
1295 case 'E': FlushBuffer();
1296 dorecalc = (!dorecalc);
1300 maxexp = minlyap; minexp = -1.0 * minlyap;
1302 redraw(exponents[frame], expind[frame], 1);
1305 case 'F': save_to_file(); break;
1306 case 'i': if (stripe_interval > 0) {
1308 if (displayplanes > 1) {
1313 case 'I': stripe_interval++;
1314 if (displayplanes > 1) {
1318 case 'K': if (minlyap > 0.05)
1321 case 'J': minlyap += 0.05;
1323 case 'm': mapindex++;
1324 if (mapindex >= NUMMAPS)
1326 map = Maps[mapindex];
1327 deriv = Derivs[mapindex];
1329 min_a = amins[mapindex];
1331 a_range = aranges[mapindex];
1333 min_b = bmins[mapindex];
1335 b_range = branges[mapindex];
1337 for (i=0;i<FUNCMAXINDEX;i++)
1338 Forcing[i] = mapindex;
1339 max_a = min_a + a_range;
1340 max_b = min_b + b_range;
1341 a_minimums[0] = min_a; b_minimums[0] = min_b;
1342 a_maximums[0] = max_a; b_maximums[0] = max_b;
1343 a_inc = a_range / (double)width;
1344 b_inc = b_range / (double)height;
1347 a = rubber_data.p_min = min_a;
1348 b = rubber_data.q_min = min_b;
1349 rubber_data.p_max = max_a;
1350 rubber_data.q_max = max_b;
1353 case 'M': if (minlyap > 0.005)
1356 case 'N': minlyap += 0.005;
1359 case 'P': negative = (!negative);
1360 FlushBuffer(); redraw(exponents[frame], expind[frame], 1);
1362 case 'r': FlushBuffer(); redraw(exponents[frame], expind[frame], 1);
1364 case 'R': FlushBuffer(); Redraw(); break;
1366 spinlength=spinlength/2;
1367 case 'S': if (displayplanes > 1)
1369 spinlength=spinlength*2; break;
1370 case 'u': go_back(); break;
1371 case 'U': go_init(); break;
1373 case 'V': print_values(); break;
1374 case 'W': if (numwheels < MAXWHEELS)
1378 if (displayplanes > 1) {
1382 case 'w': if (numwheels > 0)
1385 numwheels = MAXWHEELS;
1386 if (displayplanes > 1) {
1390 case 'x': Clear(); break;
1391 case 'X': Destroy_frame(); break;
1392 case 'z': Cycle_frames(); redraw(exponents[frame], expind[frame], 1);
1394 case 'Z': while (!XPending(dpy)) Cycle_frames();
1395 redraw(exponents[frame], expind[frame], 1); break;
1397 case 'Q': exit(0); break;
1400 case 'H': print_help(); break;
1405 /* Here's where we index into a color map. After the Lyapunov exponent is
1406 * calculated, it is used to determine what color to use for that point.
1407 * I suppose there are a lot of ways to do this. I used the following :
1408 * if it's non-negative then there's a reserved area at the lower range
1409 * of the color map that i index into. The ratio of some "minimum exponent
1410 * value" and the calculated value is used as a ratio of how high to index
1411 * into this reserved range. Usually these colors are dark red (see init_color).
1412 * If the exponent is negative, the same ratio (expo/minlyap) is used to index
1413 * into the remaining portion of the colormap (which is usually some light
1414 * shades of color or a rainbow wheel). The coloring scheme can actually make
1415 * a great deal of difference in the quality of the picture. Different colormaps
1416 * bring out different details of the dynamics while different indexing
1417 * algorithms also greatly effect what details are seen. Play around with this.
1420 sendpoint(double expo)
1423 static double tmpexpo;
1426 tmpexpo = (negative) ? expo : -1.0 * expo;
1428 if (displayplanes >1) {
1429 index = (int)(tmpexpo*lowrange/maxexp);
1430 index = (index % lowrange) + startcolor;
1436 if (displayplanes >1) {
1437 index = (int)(tmpexpo*numfreecols/minexp);
1438 index = (index % numfreecols) + mincolindex;
1443 BufferPoint(dpy, canvas, index, point.x, point.y);
1445 exponents[frame][expind[frame]++] = expo;
1446 if (point.x >= width) {
1453 if (point.y >= height)
1462 redisplay (Window w, XExposeEvent *event)
1465 * Extract the exposed area from the event and copy
1466 * from the saved pixmap to the window.
1468 XCopyArea(dpy, pixmap, canvas, Data_GC[0],
1469 event->x, event->y, event->width, event->height,
1470 event->x, event->y);
1478 unsigned int bw, d, new_w, new_h;
1480 XGetGeometry(dpy,canvas,&r,&x,&y,&new_w,&new_h,&bw,&d);
1481 if ((new_w == width) && (new_h == height))
1483 width = new_w; height = new_h;
1484 XClearWindow(dpy, canvas);
1486 XFreePixmap(dpy, pixmap);
1487 pixmap = XCreatePixmap(dpy, DefaultRootWindow(dpy),
1488 width, height, DefaultDepth(dpy, screen));
1489 a_inc = a_range / (double)width;
1490 b_inc = b_range / (double)height;
1494 a = rubber_data.p_min = min_a;
1495 b = rubber_data.q_min = min_b;
1496 rubber_data.p_max = max_a;
1497 rubber_data.q_max = max_b;
1500 for (n=0;n<MAXFRAMES;n++)
1501 if ((n <= maxframe) && (n != frame))
1509 redraw(double *exparray, int index, int cont)
1512 static int x_sav, y_sav;
1521 for (i=0;i<index;i++)
1522 sendpoint(exparray[i]);
1530 a = point.x * a_inc + min_a;
1531 b = point.y * b_inc + min_b;
1549 /* Store color pics in PPM format and monochrome in PGM */
1559 unsigned char green;
1562 struct Colormap *colormap=NULL;
1567 (struct Colormap *)malloc(sizeof(struct Colormap)*maxcolor))
1569 fprintf(stderr,"Error malloc'ing colormap array\n");
1572 outfile = fopen(outname,"w");
1578 ximage=XGetImage(dpy, pixmap, 0, 0, width, height, AllPlanes, XYPixmap);
1580 if (displayplanes > 1) {
1581 for (i=0;i<maxcolor;i++) {
1582 colormap[i].red=(unsigned char)(Colors[i].red >> 8);
1583 colormap[i].green=(unsigned char)(Colors[i].green >> 8);
1584 colormap[i].blue =(unsigned char)(Colors[i].blue >> 8);
1586 fprintf(outfile,"P%d %d %d\n",6,width,height);
1589 fprintf(outfile,"P%d %d %d\n",5,width,height);
1590 fprintf(outfile,"# settle=%d dwell=%d start_x=%f\n",settle,dwell,
1592 fprintf(outfile,"# min_a=%f a_rng=%f max_a=%f\n",min_a,a_range,max_a);
1593 fprintf(outfile,"# min_b=%f b_rng=%f max_b=%f\n",min_b,b_range,max_b);
1595 fprintf(outfile,"# pseudo-random forcing\n");
1597 fprintf(outfile,"# periodic forcing=");
1598 for (i=0;i<maxindex;i++) {
1599 fprintf(outfile,"%d",forcing[i]);
1601 fprintf(outfile,"\n");
1604 fprintf(outfile,"# periodic forcing=01\n");
1606 fprintf(outfile,"# function forcing=");
1607 for (i=0;i<funcmaxindex;i++) {
1608 fprintf(outfile,"%d",Forcing[i]);
1610 fprintf(outfile,"\n");
1612 fprintf(outfile,"%d\n",numcolors-1);
1614 for (j=0;j<height;j++)
1615 for (i=0;i<width;i++) {
1616 c = (unsigned char)XGetPixel(ximage,i,j);
1617 if (displayplanes > 1)
1618 fwrite((char *)&colormap[c],sizeof colormap[0],1,outfile);
1620 fwrite((char *)&c,sizeof c,1,outfile);
1630 minexp = maxexp = 0.0;
1632 for (i=0;i<expind[frame];i++) {
1633 if (exponents[frame][i] < minexp)
1634 minexp = exponents[frame][i];
1635 if (exponents[frame][i] > maxexp)
1636 maxexp = exponents[frame][i];
1643 XClearWindow(dpy, canvas);
1644 XCopyArea(dpy, canvas, pixmap, Data_GC[0],
1645 0, 0, width, height, 0, 0);
1653 printf("Width=%d Height=%d numcolors=%d settle=%d dwell=%d\n",
1654 width,height,numcolors,settle,dwell);
1655 printf("min_a=%f a_range=%f max_a=%f\n", min_a,a_range,max_a);
1656 printf("min_b=%f b_range=%f max_b=%f\n", min_b,b_range,max_b);
1657 printf("minlyap=%f minexp=%f maxexp=%f\n", minlyap,minexp,maxexp);
1666 values.foreground = foreground;
1667 values.line_style = LineSolid;
1668 values.function = GXxor;
1669 RubberGC = XCreateGC(dpy, DefaultRootWindow(dpy),
1670 GCForeground | GCBackground | GCFunction | GCLineStyle, &values);
1674 StartRubberBand(Window w, image_data_t *data, XEvent *event)
1679 data->rubber_band.last_x = data->rubber_band.start_x = event->xbutton.x;
1680 data->rubber_band.last_y = data->rubber_band.start_y = event->xbutton.y;
1681 SetupCorners(corners, data);
1682 XDrawLines(dpy, canvas, RubberGC,
1683 corners, sizeof(corners) / sizeof(corners[0]), CoordModeOrigin);
1687 SetupCorners(XPoint *corners, image_data_t *data)
1689 corners[0].x = data->rubber_band.start_x;
1690 corners[0].y = data->rubber_band.start_y;
1691 corners[1].x = data->rubber_band.start_x;
1692 corners[1].y = data->rubber_band.last_y;
1693 corners[2].x = data->rubber_band.last_x;
1694 corners[2].y = data->rubber_band.last_y;
1695 corners[3].x = data->rubber_band.last_x;
1696 corners[3].y = data->rubber_band.start_y;
1697 corners[4] = corners[0];
1701 TrackRubberBand(Window w, image_data_t *data, XEvent *event)
1708 SetupCorners(corners, data);
1709 XDrawLines(dpy, canvas, RubberGC,
1710 corners, sizeof(corners) / sizeof(corners[0]), CoordModeOrigin);
1711 ydiff = event->xbutton.y - data->rubber_band.start_y;
1712 xdiff = event->xbutton.x - data->rubber_band.start_x;
1713 data->rubber_band.last_x = data->rubber_band.start_x + xdiff;
1714 data->rubber_band.last_y = data->rubber_band.start_y + ydiff;
1715 if (data->rubber_band.last_y < data->rubber_band.start_y ||
1716 data->rubber_band.last_x < data->rubber_band.start_x)
1718 data->rubber_band.last_y = data->rubber_band.start_y;
1719 data->rubber_band.last_x = data->rubber_band.start_x;
1721 SetupCorners(corners, data);
1722 XDrawLines(dpy, canvas, RubberGC,
1723 corners, sizeof(corners) / sizeof(corners[0]), CoordModeOrigin);
1727 EndRubberBand(Window w, image_data_t *data, XEvent *event)
1734 SetupCorners(corners, data);
1735 XDrawLines(dpy, canvas, RubberGC,
1736 corners, sizeof(corners) / sizeof(corners[0]), CoordModeOrigin);
1737 if (data->rubber_band.start_x >= data->rubber_band.last_x ||
1738 data->rubber_band.start_y >= data->rubber_band.last_y)
1740 top.x = data->rubber_band.start_x;
1741 bot.x = data->rubber_band.last_x;
1742 top.y = data->rubber_band.start_y;
1743 bot.y = data->rubber_band.last_y;
1744 diff = data->q_max - data->q_min;
1745 delta = (double)top.y / (double)height;
1746 data->q_min += diff * delta;
1747 delta = (double)(height - bot.y) / (double)height;
1748 data->q_max -= diff * delta;
1749 diff = data->p_max - data->p_min;
1750 delta = (double)top.x / (double)width;
1751 data->p_min += diff * delta;
1752 delta = (double)(width - bot.x) / (double)width;
1753 data->p_max -= diff * delta;
1755 set_new_params(w, data);
1759 set_new_params(Window w, image_data_t *data)
1761 frame = (maxframe + 1) % MAXFRAMES;
1762 if (frame > maxframe)
1764 a_range = data->p_max - data->p_min;
1765 b_range = data->q_max - data->q_min;
1766 a_minimums[frame] = min_a = data->p_min;
1767 b_minimums[frame] = min_b = data->q_min;
1768 a_inc = a_range / (double)width;
1769 b_inc = b_range / (double)height;
1775 a_maximums[frame] = max_a = data->p_max;
1776 b_maximums[frame] = max_b = data->q_max;
1785 if (frame > maxframe)
1802 rubber_data.p_min = min_a = a_minimums[frame];
1803 rubber_data.q_min = min_b = b_minimums[frame];
1804 rubber_data.p_max = max_a = a_maximums[frame];
1805 rubber_data.q_max = max_b = b_maximums[frame];
1806 a_range = max_a - min_a;
1807 b_range = max_b - min_b;
1808 a_inc = a_range / (double)width;
1809 b_inc = b_range / (double)height;
1818 redraw(exponents[frame], expind[frame], 0);
1833 for (i=frame; i<maxframe; i++) {
1834 exponents[frame] = exponents[frame+1];
1835 expind[frame] = expind[frame+1];
1836 a_minimums[frame] = a_minimums[frame+1];
1837 b_minimums[frame] = b_minimums[frame+1];
1838 a_maximums[frame] = a_maximums[frame+1];
1839 b_maximums[frame] = b_maximums[frame+1];
1850 for (i = 0 ; i < maxcolor; ++i)
1851 Points.npoints[i] = 0;
1855 BufferPoint(Display *display, Window window, int color, int x, int y)
1857 if (Points.npoints[color] == MAXPOINTS)
1859 XDrawPoints(display, window, Data_GC[color],
1860 Points.data[color], Points.npoints[color], CoordModeOrigin);
1861 XDrawPoints(display, pixmap, Data_GC[color],
1862 Points.data[color], Points.npoints[color], CoordModeOrigin);
1863 Points.npoints[color] = 0;
1865 Points.data[color][Points.npoints[color]].x = x;
1866 Points.data[color][Points.npoints[color]].y = y;
1867 ++Points.npoints[color];
1875 for (color = 0; color < maxcolor; ++color)
1876 if (Points.npoints[color])
1878 XDrawPoints(dpy, canvas, Data_GC[color],
1879 Points.data[color], Points.npoints[color],
1881 XDrawPoints(dpy, pixmap, Data_GC[color],
1882 Points.data[color], Points.npoints[color],
1884 Points.npoints[color] = 0;
1891 printf("During run-time, interactive control can be exerted via : \n");
1892 printf("Mouse buttons allow rubber-banding of a zoom box\n");
1893 printf("< halves the 'dwell', > doubles the 'dwell'\n");
1894 printf("[ halves the 'settle', ] doubles the 'settle'\n");
1895 printf("D flushes the drawing buffer\n");
1896 printf("e or E recalculates color indices\n");
1897 printf("f or F saves exponents to a file\n");
1898 printf("h or H or ? displays this message\n");
1899 printf("i decrements, I increments the stripe interval\n");
1900 printf("KJMN increase/decrease minimum negative exponent\n");
1901 printf("m increments the map index, changing maps\n");
1902 printf("p or P reverses the colormap for negative/positive exponents\n");
1903 printf("r redraws without recalculating\n");
1904 printf("R redraws, recalculating with new dwell and settle values\n");
1905 printf("s or S spins the colorwheel\n");
1906 printf("u pops back up to the last zoom\n");
1907 printf("U pops back up to the first picture\n");
1908 printf("v or V displays the values of various settings\n");
1909 printf("w decrements, W increments the color wheel index\n");
1910 printf("x or X clears the window\n");
1911 printf("q or Q exits\n");
1919 printf("\nminlyap=%f minexp=%f maxexp=%f\n",minlyap,minexp,maxexp);
1920 printf("width=%d height=%d\n",width,height);
1921 printf("settle=%d dwell=%d start_x=%f\n",settle,dwell, start_x);
1922 printf("min_a=%f a_rng=%f max_a=%f\n",min_a,a_range,max_a);
1923 printf("min_b=%f b_rng=%f max_b=%f\n",min_b,b_range,max_b);
1925 printf("pseudo-random forcing\n");
1927 printf("periodic forcing=");
1928 for (i=0;i<maxindex;i++)
1929 printf("%d",forcing[i]);
1933 printf("periodic forcing=01\n");
1935 printf("function forcing=");
1936 for (i=0;i<funcmaxindex;i++) {
1937 printf("%d",Forcing[i]);
1941 printf("numcolors=%d\n",numcolors-1);
1949 for (i=0;i<MAXFRAMES;i++)
1958 for (i=0;i<MAXFRAMES;i++) {
1960 (double *)malloc(sizeof(double)*width*height))==NULL){
1961 fprintf(stderr,"Error malloc'ing exponent array.\n");
1971 for (i=0;i<MAXINDEX;i++)
1972 forcing[i] = (random() > prob) ? 0 : 1;