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Sebastián Santisi 1 year ago
parent 588e168273
commit e0aad1e98b
8 changed files with 282 additions and 19 deletions
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21
README.md
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# Mandelbrot
Esta es una colección de diferentes scripts para generar conjuntos de Mandelbrot.
Implementada C, con aritmética flotante de 96 y 128 bits, paralelizada en OpenMP y con interfaz sencilla en SDL2.
Los keyframes están generados en C mientras que las imágenes intermedias se interpolan con ImageMagik
## Ejemplos:
https://www.youtube.com/watch?v=j7vwzfUibwY
https://www.youtube.com/watch?v=_8ECNKlCjbw
https://www.youtube.com/watch?v=tcUKCw993Ms
### [Buddahbrots](https://es.wikipedia.org/wiki/Buddhabrot)
![](buddahbrot.png)
![](buddahbrot2.png)

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14
generate.py
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import os
s = (1920, 1080)
f = 0.5 ** (1/69)
j = 1
for x in range(5):
w = 1920.0
for i in range(69):
w /= f
width = int(w + 0.5)
print("convert img2-%05d.png -resize %dx1080^ -gravity Center -extent 1920x1080 img-%05d.png" % (x, width, 4160 + j))
os.system("convert img2-%05d.png -resize %dx1080^ -gravity Center -extent 1920x1080 img-%05d.png" % (x, width, 4160 + j))
j += 1

118
mandelbrot_buddah.c
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#include <stdint.h>
#include <math.h>
#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
#define VENTANA_ANCHO (1920*2)
#define VENTANA_ALTO (1080*2)
#define ANCHO VENTANA_ANCHO
#define ALTO VENTANA_ALTO
#define MAX_BAILOUT 50000
double xc = -0.5, yc = 0;
int bailout(double x0, double y0, double zoom) {
x0 = x0 * zoom + xc;
y0 = y0 * zoom + yc;
if(
(x0 > -1.2 && x0 <= -1.1 && y0 > -0.1 && y0 < 0.1)
|| (x0 > -1.1 && x0 <= -0.9 && y0 > -0.2 && y0 < 0.2)
|| (x0 > -0.9 && x0 <= -0.8 && y0 > -0.1 && y0 < 0.1)
|| (x0 > -0.69 && x0 <= -0.61 && y0 > -0.2 && y0 < 0.2)
|| (x0 > -0.61 && x0 <= -0.5 && y0 > -0.37 && y0 < 0.37)
|| (x0 > -0.5 && x0 <= -0.39 && y0 > -0.48 && y0 < 0.48)
|| (x0 > -0.39 && x0 <= 0.14 && y0 > -0.55 && y0 < 0.55)
|| (x0 > 0.14 && x0 < 0.29 && y0 > -0.42 && y0 < -0.07)
|| (x0 > 0.14 && x0 < 0.29 && y0 > 0.07 && y0 < 0.42)
) return MAX_BAILOUT;
double x = 0;
double y = 0;
int n = 0;
while(x*x + y*y <= 4 && n < MAX_BAILOUT) {
double xtemp = x*x - y*y + x0;
y = 2*x*y + y0;
x = xtemp;
n++;
}
return n;
}
unsigned int max(unsigned int m[ALTO][ANCHO]) {
unsigned int max = 0;
for(int i = 0; i < ALTO; i++)
for(int j = 0; j < ANCHO; j++)
if(m[i][j] > max)
max = m[i][j];
return max;
}
void computar_intensidad(unsigned int m500[ALTO][ANCHO], unsigned int m5000[ALTO][ANCHO], unsigned int m50000[ALTO][ANCHO], double x0, double y0, double zoom) {
x0 = x0 * zoom + xc;
y0 = y0 * zoom + yc;
double x = 0;
double y = 0;
int n = 0;
while(x*x + y*y <= 4 && n < MAX_BAILOUT) {
double xtemp = x*x - y*y + x0;
y = 2*x*y + y0;
x = xtemp;
int xx = (x - xc) / zoom + ANCHO / 2;
int yy = (y - yc) / zoom + ALTO / 2;
if(xx > 0 && xx < ANCHO && yy > 0 && yy < ALTO) {
if(n < 500)
m500[yy][xx]++;
if(n < 5000)
m5000[yy][xx]++;
m50000[yy][xx]++;
}
n++;
}
}
int main() {
double zoom = 1e-3;
float step = 0.1;
unsigned int (*m500)[ANCHO] = calloc(ANCHO * ALTO, sizeof(unsigned int));
unsigned int (*m5000)[ANCHO] = calloc(ANCHO * ALTO, sizeof(unsigned int));
unsigned int (*m50000)[ANCHO] = calloc(ANCHO * ALTO, sizeof(unsigned int));
for(double vy = -ALTO / 2; vy < ALTO / 2; vy += step)
for(double vx = - ANCHO / 2; vx < ANCHO / 2; vx += step) {
if(bailout(vx, vy, zoom) < MAX_BAILOUT)
computar_intensidad(m500, m5000, m50000, vx, vy, zoom);
}
int max500 = max(m500);
int max5000 = max(m5000);
int max50000 = max(m50000);
/* if(!max500) max500 = 1;
if(!max5000) max5000 = 1;
if(!max50000) max50000 = 1;*/
int mm = max500;
if(max5000 > mm)
mm = max5000;
if(max50000 > mm)
mm = max50000;
printf("P3\n%d %d\n%d\n", ALTO, ANCHO, mm);
for(int i = 0; i < ANCHO; i++)
for(int j = 0; j < ALTO; j++)
printf("%u %u %u\n",
m50000[j][i], //* 255 / max50000,
m5000[j][i], //* 255 / max5000,
m500[j][i] //* 255 / max500
);
return 0;
}

13
mandelbrot_main.c
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#include <sys/time.h>
#define VENTANA_ANCHO 300
#define VENTANA_ALTO 200
#define VENTANA_ANCHO 800
#define VENTANA_ALTO 600
#define ANCHO VENTANA_ANCHO
#define ALTO VENTANA_ALTO
#define MAX_ITER 10000
#define MAX_ITER 500
#define JUEGO_FPS 10
static double time_in_ms(void) {
@ -22,8 +22,7 @@ static double time_in_ms(void) {
//long double xc = -1.740119020442992652289958266376L;
//long double yc = 0.028019209975637676263081582255L;
//long double xc = 0.264226442163892496529931097626331393L, yc = 0.002572261418806922467217290773078275L; // Video 2
long double xc = -1.749900374662927212679117139337847675L, yc = 0.000000000002454985822810237255224056L;
long double xc = 0.264226442163892496529931097626331393L, yc = 0.002572261418806922467217290773078275;
uint32_t computar_intensidad(long double x0, long double y0, long double zoom) {
//x0 = x0 * zoom - 1.7400623825793398724575; // Derecha: Achicar
@ -46,7 +45,7 @@ uint32_t computar_intensidad(long double x0, long double y0, long double zoom) {
return 0;
//float h = (n + 1 - log(log2(sqrt(x*x+y*y)))) / MAX_ITER * 360;
float h = (int)(n * 360.0 / 100) % 360;
float h = (int)(n * 360.0 / 50) % 360;
float xxx = (1 - fabs(fmodf(h / 60.0, 2) - 1));
uint8_t xx = (xxx < 1 ? xxx : 1) * 255;
uint8_t r = 0, g = 0, b = 0;
@ -154,7 +153,7 @@ int width, height;
for(int vx = - ANCHO / 2; vx < ANCHO / 2; vx++) {
canvas[i++] = computar_intensidad(vx, vy, zoom);
}
printf("%f %.5Le\nlong double xc = %.36LfL, yc = %.36LfL;\n", time_in_ms() - begin, zoom, xc, yc);
printf("%f %.5Le %.36Lf %.36Lf\n", time_in_ms() - begin, zoom, xc, yc);
// Implementar imagen_a_textura() cuanto antes!

21
mandelbrot_png.c
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#include <stdio.h>
#include <stdlib.h>
#include <omp.h>
#define PREFIX "img-"
#define VENTANA_ANCHO 1920
@ -66,17 +64,14 @@ int main() {
long double zoom = 0.179;
double factor = 0.99;
size_t n = 0;
for(double z = zoom; z >= 1e-20; z *= factor)
n++;
int i = 0;
double *zooms = malloc(n * sizeof(double));
zooms[0] = zoom;
for(size_t i = 1; i < n; i++)
zooms[i] = zooms[i - 1] * factor;
while(1) {
if(zoom < 1e-20)
break;
zoom *= factor;
#pragma omp parallel for schedule(dynamic)
for(int i = 0; i < n; i++) {
printf("%d\n", i);
char aux[100];
@ -87,13 +82,15 @@ int main() {
for(int vy = ALTO / 2; vy > - ALTO / 2; vy--)
for(int vx = - ANCHO / 2; vx < ANCHO / 2; vx++) {
uint32_t c = computar_intensidad(vx, vy, zooms[i]);
uint32_t c = computar_intensidad(vx, vy, zoom);
fprintf(f, "%d %d %d\n", c >> 24, (c >> 16) & 0xFF, (c >> 8) & 0xFF);
}
fclose(f);
sprintf(aux, "convert %s%05d.ppm %s%05d.png; rm %s%05d.ppm", PREFIX, i, PREFIX, i, PREFIX, i);
system(aux);
i++;
}
system("ffmpeg -y -framerate 24 -i " PREFIX "%05d.png -c:v libx264 -crf 0 output.mp4");

114
mandelbrot_png_openmp.c
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#include <stdint.h>
#include <math.h>
#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
#include <quadmath.h>
#include <omp.h>
#define PREFIX "img2-"
#define VENTANA_ANCHO (1920*2)
#define VENTANA_ALTO (1080*2)
#define ANCHO VENTANA_ANCHO
#define ALTO VENTANA_ALTO
#define MAX_ITER 10000 //500 en video2
//__float128 xc = -1.740119020442992652289958266376L;
//__float128 yc = 0.028019209975637676263081582255L;
//__float128 xc = 0.264226442163892496529931097626331393L, yc = 0.002572261418806922467217290773078275;
__float128 xc = -1.749900374662927212679117139337847675Q, yc = 0.000000000002454985822810237255224056Q;
uint32_t computar_intensidad(__float128 x0, __float128 y0, __float128 zoom) {
//x0 = x0 * zoom - 1.7400623825793398724575; // Derecha: Achicar
//y0 = y0 * zoom + 0.0281753397792111; // Abajo: Achicar
x0 = x0 * zoom + xc; // Derecha: Achicar
y0 = y0 * zoom + yc; // Abajo: Achicar
//x0 = x0 * zoom - 1.78; // Derecha: Achicar
//y0 = y0 * zoom + 0.0; // Abajo: Achicar
__float128 x = 0;
__float128 y = 0;
int n = 0;
while(x*x + y*y <= 4 && n < MAX_ITER) {
__float128 xtemp = x*x - y*y + x0;
y = 2*x*y + y0;
x = xtemp;
n++;
}
if(n == MAX_ITER)
return 0;
//float h = (n + 1 - log(log2(sqrt(x*x+y*y)))) / MAX_ITER * 360;
//float h = n * 360.0 / MAX_ITER;
float h = (int)(n * 360.0 / 100) % 360;
float xxx = (1 - fabs(fmodf(h / 60.0, 2) - 1));
uint8_t xx = (xxx < 1 ? xxx : 1) * 255;
uint8_t r = 0, g = 0, b = 0;
if(h < 60)
r = 255, g = xx;
else if(h < 120)
g = 255, r = xx;
else if(h < 180)
g = 255, b = xx;
else if(h < 240)
b = 255, g = xx;
else if(h < 300)
b = 255, r = xx;
else
r = 255, b = xx;
return (r << 24) | (g << 16) | (b << 8);
}
int main() {
__float128 zoom = 0.179;
double factor = 0.99;
size_t n = 0;
for(double z = zoom; z >= 1e-21; z *= factor)
n++;
double *zooms = malloc(n * sizeof(double));
zooms[0] = zoom;
for(size_t i = 1; i < n; i++)
zooms[i] = zooms[i - 1] * factor;
zooms[0] = zooms[4160] * 0.5;
printf("%.16e\n", zooms[4160]);
n = 6;
for(size_t i = 1; i < n; i++)
zooms[i] = zooms[i - 1] * 0.5;
#pragma omp parallel for schedule(dynamic)
for(int i = 0; i < n; i++) {
printf("%d %.16e\n", i, zooms[i]);
char aux[100];
sprintf(aux, "%s%05d.ppm", PREFIX, i);
FILE *f = fopen(aux, "wt");
fprintf(f, "P3\n%d %d\n255\n", ANCHO, ALTO);
for(int vy = ALTO / 2; vy > - ALTO / 2; vy--)
for(int vx = - ANCHO / 2; vx < ANCHO / 2; vx++) {
uint32_t c = computar_intensidad(vx, vy, zooms[i]);
fprintf(f, "%d %d %d\n", c >> 24, (c >> 16) & 0xFF, (c >> 8) & 0xFF);
}
fclose(f);
sprintf(aux, "convert %s%05d.ppm %s%05d.png; rm %s%05d.ppm", PREFIX, i, PREFIX, i, PREFIX, i);
system(aux);
}
free(zooms);
// system("ffmpeg -y -framerate 24 -i " PREFIX "%05d.png -c:v libx264 -crf 0 output.mp4");
return 0;
}
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