write a C example use Newton-Raphson to get Fractrals for f(z)=z^3-1=0 and save the result into "Problem1.txt"
时间: 2023-05-22 16:04:05 浏览: 57
Sure, here's a C example that uses Newton-Raphson method to get fractals for f(z) = z^3 - 1 = 0:
```c
#include <stdio.h>
#include <math.h>
#define MAX_ITER 1000
#define EPSILON 1e-6
typedef struct {
double x;
double y;
} Complex;
void newton_raphson(Complex z, Complex *z_new) {
Complex numerator = {pow(z.x, 3) + 3 * z.x * pow(z.y, 2) - 1, 3 * pow(z.x, 2) * z.y - pow(z.y, 3)};
Complex denominator = {3 * pow(z.x, 2) + 3 * pow(z.y, 2), 6 * z.x * z.y};
z_new->x = z.x - numerator.x / denominator.x;
z_new->y = z.y - numerator.y / denominator.y;
}
int main() {
FILE *fp;
fp = fopen("Problem1.txt", "w");
if (fp == NULL) {
printf("Error opening file\n");
return 1;
}
for (double x = -2; x <= 2; x += 0.01) {
for (double y = -2; y <= 2; y += 0.01) {
Complex z = {x, y};
Complex z_new = {0, 0};
int iter = 0;
while (iter < MAX_ITER) {
newton_raphson(z, &z_new);
double distance = sqrt(pow(z_new.x - z.x, 2) + pow(z_new.y - z.y, 2));
if (distance < EPSILON) {
fprintf(fp, "%.2lf %.2lf\n", x, y);
break;
}
z = z_new;
iter++;
}
}
}
fclose(fp);
return 0;
}
```
This code performs a double loop over the region from -2 to 2 in both the x and y dimensions with a step size of 0.01. For each point (x, y), the code applies the Newton-Raphson method to find the root of the equation f(z) = z^3 - 1 starting from the initial point z = (x, y). The method is iterated until either the maximum number of iterations is reached (MAX_ITER) or the distance between successive iterations is below a small tolerance (EPSILON).
If the root is found, the point (x, y) is considered to be part of the fractal and is written to the file "Problem1.txt" in the format "x y".
Note that this code makes use of complex arithmetic and is fairly computationally intensive, so it may take a while to run depending on your machine.