1 | /* -*- Mode: C; tab-width: 4 -*- */ |
---|
2 | /* discrete --- chaotic mappings */ |
---|
3 | |
---|
4 | #if 0 |
---|
5 | static const char sccsid[] = "@(#)discrete.c 5.00 2000/11/01 xlockmore"; |
---|
6 | #endif |
---|
7 | |
---|
8 | /*- |
---|
9 | * Copyright (c) 1996 by Tim Auckland <Tim.Auckland@Procket.com> |
---|
10 | * |
---|
11 | * Permission to use, copy, modify, and distribute this software and its |
---|
12 | * documentation for any purpose and without fee is hereby granted, |
---|
13 | * provided that the above copyright notice appear in all copies and that |
---|
14 | * both that copyright notice and this permission notice appear in |
---|
15 | * supporting documentation. |
---|
16 | * |
---|
17 | * This file is provided AS IS with no warranties of any kind. The author |
---|
18 | * shall have no liability with respect to the infringement of copyrights, |
---|
19 | * trade secrets or any patents by this file or any part thereof. In no |
---|
20 | * event will the author be liable for any lost revenue or profits or |
---|
21 | * other special, indirect and consequential damages. |
---|
22 | * |
---|
23 | * "discrete" shows a number of fractals based on the "discrete map" |
---|
24 | * type of dynamical systems. They include a different way of looking |
---|
25 | * at the HOPALONG system, an inverse julia-set iteration, the "Standard |
---|
26 | * Map" and the "Bird in a Thornbush" fractal. |
---|
27 | * |
---|
28 | * Revision History: |
---|
29 | * 01-Nov-2000: Allocation checks |
---|
30 | * 31-Jul-1997: Ported to xlockmore-4 |
---|
31 | * 08-Aug-1996: Adapted from hop.c Copyright (c) 1991 by Patrick J. Naughton. |
---|
32 | */ |
---|
33 | |
---|
34 | #ifdef STANDALONE |
---|
35 | #define MODE_discrete |
---|
36 | #define PROGCLASS "Discrete" |
---|
37 | #define HACK_INIT init_discrete |
---|
38 | #define HACK_DRAW draw_discrete |
---|
39 | #define discrete_opts xlockmore_opts |
---|
40 | #define DEFAULTS "*delay: 1000 \n" \ |
---|
41 | "*count: 4096 \n" \ |
---|
42 | "*cycles: 2500 \n" \ |
---|
43 | "*ncolors: 100 \n" |
---|
44 | #define SMOOTH_COLORS |
---|
45 | #include "xlockmore.h" /* in xscreensaver distribution */ |
---|
46 | #include "erase.h" |
---|
47 | #else /* STANDALONE */ |
---|
48 | #include "xlock.h" /* in xlockmore distribution */ |
---|
49 | #endif /* STANDALONE */ |
---|
50 | |
---|
51 | #ifdef MODE_discrete |
---|
52 | |
---|
53 | ModeSpecOpt discrete_opts = |
---|
54 | {0, (XrmOptionDescRec *) NULL, 0, (argtype *) NULL, (OptionStruct *) NULL}; |
---|
55 | |
---|
56 | #ifdef USE_MODULES |
---|
57 | ModStruct discrete_description = |
---|
58 | {"discrete", "init_discrete", "draw_discrete", "release_discrete", |
---|
59 | "refresh_discrete", "init_discrete", (char *) NULL, &discrete_opts, |
---|
60 | 1000, 4096, 2500, 1, 64, 1.0, "", |
---|
61 | "Shows various discrete maps", 0, NULL}; |
---|
62 | |
---|
63 | #endif |
---|
64 | |
---|
65 | enum ftypes { |
---|
66 | SQRT, BIRDIE, STANDARD, TRIG, CUBIC, HENON, AILUJ, HSHOE, DELOG |
---|
67 | }; |
---|
68 | |
---|
69 | /*#define TEST STANDARD */ |
---|
70 | |
---|
71 | #define BIASES 18 |
---|
72 | static enum ftypes bias[BIASES] = |
---|
73 | { |
---|
74 | STANDARD, STANDARD, STANDARD, STANDARD, |
---|
75 | SQRT, SQRT, SQRT, SQRT, |
---|
76 | BIRDIE, BIRDIE, BIRDIE, |
---|
77 | AILUJ, AILUJ, AILUJ, |
---|
78 | TRIG, TRIG, |
---|
79 | CUBIC, |
---|
80 | HENON, |
---|
81 | }; |
---|
82 | |
---|
83 | typedef struct { |
---|
84 | int maxx; |
---|
85 | int maxy; /* max of the screen */ |
---|
86 | double a; |
---|
87 | double b; |
---|
88 | double c; |
---|
89 | double d; |
---|
90 | double e; |
---|
91 | double i; |
---|
92 | double j; /* discrete parameters */ |
---|
93 | double ic; |
---|
94 | double jc; |
---|
95 | double is; |
---|
96 | double js; |
---|
97 | int inc; |
---|
98 | int pix; |
---|
99 | enum ftypes op; |
---|
100 | int count; |
---|
101 | XPoint *pointBuffer; /* pointer for XDrawPoints */ |
---|
102 | } discretestruct; |
---|
103 | |
---|
104 | static discretestruct *discretes = (discretestruct *) NULL; |
---|
105 | |
---|
106 | void |
---|
107 | init_discrete(ModeInfo * mi) |
---|
108 | { |
---|
109 | double range; |
---|
110 | discretestruct *hp; |
---|
111 | |
---|
112 | if (discretes == NULL) { |
---|
113 | if ((discretes = |
---|
114 | (discretestruct *) calloc(MI_NUM_SCREENS(mi), |
---|
115 | sizeof (discretestruct))) == NULL) |
---|
116 | return; |
---|
117 | } |
---|
118 | hp = &discretes[MI_SCREEN(mi)]; |
---|
119 | |
---|
120 | hp->maxx = MI_WIDTH(mi); |
---|
121 | hp->maxy = MI_HEIGHT(mi); |
---|
122 | #ifdef TEST |
---|
123 | hp->op = TEST; |
---|
124 | #else |
---|
125 | hp->op = bias[LRAND() % BIASES]; |
---|
126 | #endif |
---|
127 | switch (hp->op) { |
---|
128 | case HSHOE: |
---|
129 | hp->ic = 0; |
---|
130 | hp->jc = 0; |
---|
131 | hp->is = hp->maxx / (4); |
---|
132 | hp->js = hp->maxy / (4); |
---|
133 | hp->a = 0.5; |
---|
134 | hp->b = 0.5; |
---|
135 | hp->c = 0.2; |
---|
136 | hp->d = -1.25; |
---|
137 | hp->e = 1; |
---|
138 | hp->i = hp->j = 0.0; |
---|
139 | break; |
---|
140 | case DELOG: |
---|
141 | hp->ic = 0.5; |
---|
142 | hp->jc = 0.3; |
---|
143 | hp->is = hp->maxx / 1.5; |
---|
144 | hp->js = hp->maxy / 1.5; |
---|
145 | hp->a = 2.176399; |
---|
146 | hp->i = hp->j = 0.01; |
---|
147 | break; |
---|
148 | case HENON: |
---|
149 | hp->jc = ((LRAND() / MAXRAND) * 2.0 - 1.0) * 0.4; |
---|
150 | hp->ic = 1.3 * (1 - (hp->jc * hp->jc) / (0.4 * 0.4)); |
---|
151 | hp->is = hp->maxx; |
---|
152 | hp->js = hp->maxy * 1.5; |
---|
153 | hp->a = 1; |
---|
154 | hp->b = 1.4; |
---|
155 | hp->c = 0.3; |
---|
156 | hp->i = hp->j = 0; |
---|
157 | break; |
---|
158 | case SQRT: |
---|
159 | hp->ic = 0; |
---|
160 | hp->jc = 0; |
---|
161 | hp->is = 1; |
---|
162 | hp->js = 1; |
---|
163 | range = sqrt((double) hp->maxx * 2 * hp->maxx * 2 + |
---|
164 | (double) hp->maxy * 2 * hp->maxy * 2) / |
---|
165 | (10.0 + LRAND() % 10); |
---|
166 | |
---|
167 | hp->a = (LRAND() / MAXRAND) * range - range / 2.0; |
---|
168 | hp->b = (LRAND() / MAXRAND) * range - range / 2.0; |
---|
169 | hp->c = (LRAND() / MAXRAND) * range - range / 2.0; |
---|
170 | if (!(LRAND() % 2)) |
---|
171 | hp->c = 0.0; |
---|
172 | hp->i = hp->j = 0.0; |
---|
173 | break; |
---|
174 | case STANDARD: |
---|
175 | hp->ic = M_PI; |
---|
176 | hp->jc = M_PI; |
---|
177 | hp->is = hp->maxx / (M_PI * 2); |
---|
178 | hp->js = hp->maxy / (M_PI * 2); |
---|
179 | hp->a = 0; /* decay */ |
---|
180 | hp->b = (LRAND() / MAXRAND) * 2.0; |
---|
181 | hp->c = 0; |
---|
182 | hp->i = M_PI; |
---|
183 | hp->j = M_PI; |
---|
184 | break; |
---|
185 | case BIRDIE: |
---|
186 | hp->ic = 0; |
---|
187 | hp->jc = 0; |
---|
188 | hp->is = hp->maxx / 2; |
---|
189 | hp->js = hp->maxy / 2; |
---|
190 | hp->a = 1.99 + ((LRAND() / MAXRAND) * 2.0 - 1.0) * 0.2; |
---|
191 | hp->b = 0; |
---|
192 | hp->c = 0.8 + ((LRAND() / MAXRAND) * 2.0 - 1.0) * 0.1; |
---|
193 | hp->i = hp->j = 0; |
---|
194 | break; |
---|
195 | case TRIG: |
---|
196 | hp->a = 5; |
---|
197 | hp->b = 0.5 + ((LRAND() / MAXRAND) * 2.0 - 1.0) * 0.3; |
---|
198 | hp->ic = hp->a; |
---|
199 | hp->jc = 0; |
---|
200 | hp->is = hp->maxx / (hp->b * 20); |
---|
201 | hp->js = hp->maxy / (hp->b * 20); |
---|
202 | hp->i = hp->j = 0; |
---|
203 | break; |
---|
204 | case CUBIC: |
---|
205 | hp->a = 2.77; |
---|
206 | hp->b = 0.1 + ((LRAND() / MAXRAND) * 2.0 - 1.0) * 0.1; |
---|
207 | hp->ic = 0; |
---|
208 | hp->jc = 0; |
---|
209 | hp->is = hp->maxx / 4; |
---|
210 | hp->js = hp->maxy / 4; |
---|
211 | hp->i = hp->j = 0.1; |
---|
212 | break; |
---|
213 | case AILUJ: |
---|
214 | { |
---|
215 | int i; |
---|
216 | double x, y, xn, yn; |
---|
217 | |
---|
218 | hp->ic = 0; |
---|
219 | hp->jc = 0; |
---|
220 | hp->is = hp->maxx / 4; |
---|
221 | hp->js = hp->maxx / 4; |
---|
222 | do { |
---|
223 | hp->a = ((LRAND() / MAXRAND) * 2.0 - 1.0) * 1.5 - 0.5; |
---|
224 | hp->b = ((LRAND() / MAXRAND) * 2.0 - 1.0) * 1.5; |
---|
225 | x = y = 0; |
---|
226 | #define MAXITER 10 |
---|
227 | for (i = 0; i < MAXITER && x * x + y * y < 13; i++) { /* 'Brot calc */ |
---|
228 | xn = x * x - y * y + hp->a; |
---|
229 | yn = 2 * x * y + hp->b; |
---|
230 | x = xn; |
---|
231 | y = yn; |
---|
232 | } |
---|
233 | } while (i < MAXITER); /* wait for a connected set */ |
---|
234 | hp->i = hp->j = 0.1; |
---|
235 | break; |
---|
236 | } |
---|
237 | } |
---|
238 | hp->pix = 0; |
---|
239 | hp->inc = 0; |
---|
240 | |
---|
241 | if (hp->pointBuffer == NULL) { |
---|
242 | hp->pointBuffer = (XPoint *) malloc(sizeof (XPoint) * MI_COUNT(mi)); |
---|
243 | /* if fails will check later */ |
---|
244 | } |
---|
245 | |
---|
246 | /* Clear the background. */ |
---|
247 | MI_CLEARWINDOW(mi); |
---|
248 | |
---|
249 | XSetForeground(MI_DISPLAY(mi), MI_GC(mi), MI_WHITE_PIXEL(mi)); |
---|
250 | hp->count = 0; |
---|
251 | } |
---|
252 | |
---|
253 | |
---|
254 | void |
---|
255 | draw_discrete(ModeInfo * mi) |
---|
256 | { |
---|
257 | Display *dsp = MI_DISPLAY(mi); |
---|
258 | Window win = MI_WINDOW(mi); |
---|
259 | double oldj, oldi; |
---|
260 | int count = MI_COUNT(mi); |
---|
261 | int cycles = MI_CYCLES(mi); |
---|
262 | int k; |
---|
263 | XPoint *xp; |
---|
264 | GC gc = MI_GC(mi); |
---|
265 | discretestruct *hp; |
---|
266 | |
---|
267 | if (discretes == NULL) |
---|
268 | return; |
---|
269 | hp = &discretes[MI_SCREEN(mi)]; |
---|
270 | if (hp->pointBuffer == NULL) |
---|
271 | return; |
---|
272 | |
---|
273 | k = count; |
---|
274 | xp = hp->pointBuffer; |
---|
275 | |
---|
276 | hp->inc++; |
---|
277 | |
---|
278 | MI_IS_DRAWN(mi) = True; |
---|
279 | |
---|
280 | if (MI_NPIXELS(mi) > 2) { |
---|
281 | XSetForeground(dsp, gc, MI_PIXEL(mi, hp->pix)); |
---|
282 | if (++hp->pix >= MI_NPIXELS(mi)) |
---|
283 | hp->pix = 0; |
---|
284 | } |
---|
285 | while (k--) { |
---|
286 | oldj = hp->j; |
---|
287 | oldi = hp->i; |
---|
288 | switch (hp->op) { |
---|
289 | case HSHOE: |
---|
290 | { |
---|
291 | int i; |
---|
292 | |
---|
293 | #if 0 |
---|
294 | if (!k) { |
---|
295 | XSetForeground(dsp, gc, MI_BLACK_PIXEL(mi)); |
---|
296 | XFillRectangle(dsp, win, gc, 0, 0, hp->maxx, hp->maxy); |
---|
297 | XSetForeground(dsp, gc, MI_PIXEL(mi, hp->pix)); |
---|
298 | } else |
---|
299 | #endif |
---|
300 | #define HD |
---|
301 | #ifdef HD |
---|
302 | if (k < count / 4) { |
---|
303 | hp->i = ((double) k / count) * 8 - 1; |
---|
304 | hp->j = 1; |
---|
305 | } else if (k < count / 2) { |
---|
306 | hp->i = 1; |
---|
307 | hp->j = 3 - ((double) k / count) * 8; |
---|
308 | } else if (k < 3 * count / 4) { |
---|
309 | hp->i = 5 - ((double) k / count) * 8; |
---|
310 | hp->j = -1; |
---|
311 | } else { |
---|
312 | hp->i = -1; |
---|
313 | hp->j = ((double) k / count) * 8 - 7; |
---|
314 | } |
---|
315 | for (i = 1; i < (hp->inc % 15); i++) { |
---|
316 | oldj = hp->j; |
---|
317 | oldi = hp->i; |
---|
318 | #endif |
---|
319 | hp->i = (hp->a * oldi + hp->b) * oldj; |
---|
320 | hp->j = (hp->e - hp->d + hp->c * oldi) * oldj * oldj - hp->c * oldi + hp->d; |
---|
321 | #ifdef HD |
---|
322 | } |
---|
323 | #endif |
---|
324 | break; |
---|
325 | } |
---|
326 | case DELOG: |
---|
327 | hp->j = oldi; |
---|
328 | hp->i = hp->a * oldi * (1 - oldj); |
---|
329 | break; |
---|
330 | case HENON: |
---|
331 | hp->i = oldj + hp->a - hp->b * oldi * oldi; |
---|
332 | hp->j = hp->c * oldi; |
---|
333 | break; |
---|
334 | case SQRT: |
---|
335 | if (k) { |
---|
336 | hp->j = hp->a + hp->i; |
---|
337 | hp->i = -oldj + (hp->i < 0 |
---|
338 | ? sqrt(fabs(hp->b * (hp->i - hp->c))) |
---|
339 | : -sqrt(fabs(hp->b * (hp->i - hp->c)))); |
---|
340 | } else { |
---|
341 | static int s = 1; |
---|
342 | |
---|
343 | hp->i = s * hp->inc * hp->maxx / cycles / 2; |
---|
344 | hp->j = hp->a + hp->i; |
---|
345 | s = -s; |
---|
346 | } |
---|
347 | break; |
---|
348 | case STANDARD: |
---|
349 | if (k) { |
---|
350 | hp->j = (1 - hp->a) * oldj + hp->b * sin(oldi) + hp->a * hp->c; |
---|
351 | hp->j = fmod(hp->j + 2 * M_PI, 2 * M_PI); |
---|
352 | hp->i = oldi + hp->j; |
---|
353 | hp->i = fmod(hp->i + 2 * M_PI, 2 * M_PI); |
---|
354 | } else { |
---|
355 | static int s = 1; |
---|
356 | |
---|
357 | hp->j = M_PI + fmod(s * hp->inc * 2 * M_PI / (cycles - 0.5), M_PI); |
---|
358 | hp->i = M_PI; |
---|
359 | s = -s; |
---|
360 | } |
---|
361 | break; |
---|
362 | case BIRDIE: |
---|
363 | hp->j = oldi; |
---|
364 | hp->i = (1 - hp->c) * cos(M_PI * hp->a * oldj) + hp->c * hp->b; |
---|
365 | hp->b = oldj; |
---|
366 | break; |
---|
367 | case TRIG: |
---|
368 | { |
---|
369 | double r2 = oldi * oldi + oldj * oldj; |
---|
370 | |
---|
371 | hp->i = hp->a + hp->b * (oldi * cos(r2) - oldj * sin(r2)); |
---|
372 | hp->j = hp->b * (oldj * cos(r2) + oldi * sin(r2)); |
---|
373 | } |
---|
374 | break; |
---|
375 | case CUBIC: |
---|
376 | hp->i = oldj; |
---|
377 | hp->j = hp->a * oldj - oldj * oldj * oldj - hp->b * oldi; |
---|
378 | break; |
---|
379 | case AILUJ: |
---|
380 | hp->i = ((LRAND() < MAXRAND / 2) ? -1 : 1) * |
---|
381 | sqrt(((oldi - hp->a) + |
---|
382 | sqrt((oldi - hp->a) * (oldi - hp->a) + (oldj - hp->b) * (oldj - hp->b))) / 2); |
---|
383 | if (hp->i < 0.00000001 && hp->i > -0.00000001) |
---|
384 | hp->i = (hp->i > 0.0) ? 0.00000001 : -0.00000001; |
---|
385 | hp->j = (oldj - hp->b) / (2 * hp->i); |
---|
386 | break; |
---|
387 | } |
---|
388 | xp->x = hp->maxx / 2 + (int) ((hp->i - hp->ic) * hp->is); |
---|
389 | xp->y = hp->maxy / 2 - (int) ((hp->j - hp->jc) * hp->js); |
---|
390 | xp++; |
---|
391 | } |
---|
392 | XDrawPoints(dsp, win, gc, hp->pointBuffer, count, CoordModeOrigin); |
---|
393 | if (++hp->count > cycles) { |
---|
394 | #ifdef STANDALONE |
---|
395 | erase_full_window(MI_DISPLAY(mi), MI_WINDOW(mi)); |
---|
396 | #endif /* STANDALONE */ |
---|
397 | init_discrete(mi); |
---|
398 | } |
---|
399 | } |
---|
400 | |
---|
401 | void |
---|
402 | release_discrete(ModeInfo * mi) |
---|
403 | { |
---|
404 | if (discretes != NULL) { |
---|
405 | int screen; |
---|
406 | |
---|
407 | for (screen = 0; screen < MI_NUM_SCREENS(mi); screen++) { |
---|
408 | discretestruct *hp = &discretes[screen]; |
---|
409 | |
---|
410 | if (hp->pointBuffer != NULL) { |
---|
411 | (void) free((void *) hp->pointBuffer); |
---|
412 | /* hp->pointBuffer = NULL; */ |
---|
413 | } |
---|
414 | } |
---|
415 | (void) free((void *) discretes); |
---|
416 | discretes = (discretestruct *) NULL; |
---|
417 | } |
---|
418 | } |
---|
419 | |
---|
420 | void |
---|
421 | refresh_discrete(ModeInfo * mi) |
---|
422 | { |
---|
423 | MI_CLEARWINDOW(mi); |
---|
424 | } |
---|
425 | |
---|
426 | #endif /* MODE_discrete */ |
---|