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#include <complex.h>
#include <stddef.h>
#include <stdint.h>
#include <stdio.h>
#include <unistd.h>
#include <stdlib.h>
#include "grids.h"
/*
* Computes the number of iterations it takes for a point z0 to diverge
* if the return value is equal to max_iterations, the point lies within the mandelbrot set
* This is an implementation the escape algorithm
*/
size_t mandelbrot(const double complex z0, const size_t max_iterations) {
double complex z = z0;
size_t iteration = 0;
while (cabs(z) <= 2 && iteration < max_iterations) {
z = z * z + z0;
iteration++;
}
return iteration;
}
/*
* Computes the number of iterations it takes for a point z0 to diverge
* if the return value is equal to max_iterations, the point lies within the multibrot set
* This is implementation closely matches mandelbrot
* Note, only positive integer powers are supported
*/
size_t multibrot(const double complex z0, const size_t max_iterations, const uintmax_t d){
double complex z = z0;
double complex ztemp;
size_t iteration = 0;
while(cabs(z) <= 2 && iteration < max_iterations){
ztemp = z;
for(size_t i = 0; i < d; i ++){
ztemp *= ztemp;
}
z = ztemp + z0;
iteration++;
}
return iteration;
}
/*
* Converts a grid point into an complex number
*/
double complex lattice_to_complex(const size_t index, const size_t x_res, const size_t y_res) {
const double x_min = -2.0;
const double x_max = 2.0;
const double y_min = -2.0;
const double y_max = 2.0;
const double x_step = (x_max - x_min) / (double)x_res;
const double y_step = (y_max - y_min) / (double)y_res;
const size_t x_index = index % x_res;
const size_t y_index = index / x_res;
const double x = x_min + x_index * x_step;
const double y = y_min + y_index * y_step;
return x + y * I;
}
int main(const int argc, char *argv[]) {
//default values
size_t iterations = 1000;
size_t x_res = 100;
size_t y_res = 100;
//parse command line arguments
int opt;
while((opt =getopt(argc, argv, "i:x:y:")) != -1){
switch(opt){
case 'i':
iterations = strtoull(optarg, NULL, 10);
break;
case 'x':
x_res = strtoull(optarg, NULL, 10);
break;
case 'y':
y_res = strtoull(optarg, NULL, 10);
break;
default:
fprintf(stderr, "Usage: %s [-i iterations] [-x x_res] [-y y_res]\n", argv[0]);
return 1;
}
}
grid_t* grid = create_grid(x_res, y_res);
if(!grid) return 1;
const size_t size = grid->size;
size_t* data = grid->data;
for(size_t i = 0; i < size;i++){
data[i] = multibrot(lattice_to_complex(i, x_res, y_res), iterations, 3);
}
for(size_t i = 0; i < size; i++){
printf("%zu%s", data[i], (i % x_res == x_res - 1) ? "\n" : "\t");
}
}
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