Mandelbrot

As the logistic function the mandelbrot set depends on one variable, although a complex variable with its imaginary and real part:

```

```

The important part is the orbit stability or if it stays bounded, that can be obtained by iterating a predetermined number with, e.g., a C function. The orbit is unstable if tends to infinity, the c function will ignore an orbit if surpasses a known limit:

The condition sets the Mandelbrot boundary,The iteration counts can be used into an RGB color map, the image and its colors obtained with the c function emphasizes the boundary and its depth showing how many times the magnitude(|z|) keeps inside the chosen limit. Now comes the last step, making the plot.

Library:

```#include < stdio.h >
#include < math.h >
#include < stdlib.h >```

M:

`#define M 20`

A structure and a local function:

```struct complex
{
double re, im;
}x, c;

double module(struct complex x)
{
return sqrt(x.re*x.re +x.im*x.im);
}```

An the main function:

```int main(int argc, char** argv)
{
double xx;
int n, count;
struct complex;

FILE *fout;
fout=fopen("Mandelbrot.dat", "w");```

The final part you have to itinerate the function adding up how many times falls inside the limit condition - the “for ” or a “while” structure will do the job -, using a rectangle with steps of 0.005. As an example:

`Re  , Im `

The file will be generated using:

`fprintf(fout, "%gt %g %dn", c.re, c.im, count);`

The linux user will open the file by typing in his terminal:

`Plot [-2:0.5][-1:1] 'mandelbrot.dat' u 1:2:3 w image`