less_retarded_wiki/mandelbrot_set.md

# Mandelbrot Set

TODO

```
 ___________________________________________________________
|[-2,1]                                       .             |
|                                            .:.            |
|                                           :::::           |
|                                         ...:::..  .       |
|                                    :..:::::::::::::....   |
|                                   .:::::::::::::::::::'   |
|                                 ::::::::::::::::::::::::  |
|                                :::::::::::::::::::::::::' |
|                     :..:::.   .:::::::::::::::::::::::::: |
|                   .:::::::::. ::::::::::::::::::::::::::  |
|                .. ::::::::::: :::::::::::::::::::::::::'  |
|      '  '     '::':::::::::::'::::::::::::::::::::::::.   |
|                   ::::::::::: ::::::::::::::::::::::::::  |
|                    ':::::::'  ::::::::::::::::::::::::::. |
|                     '  '''     :::::::::::::::::::::::::' |
|                                '::::::::::::::::::::::::' |
|                                 ''::::::::::::::::::::''  |
|                                    ::::::::::::::::::::   |
|                                    '  ''::::::::'':       |
|                                           .:::.           |
|                                           ':::'           |
|                                             :             |
|___________________________________________________[0.5,-1]|
```

## Code

The following code is a simple [C](c.md) program that renders the Mandelbrot set into terminal (for demonstrative purposes, it isn't efficient or do any [antialiasing](antialiasing.md)).

```
#include <stdio.h>

#define ROWS 30
#define COLS 60
#define FROM_X -2.0
#define FROM_Y 1.0
#define STEP (2.5 / ((double) COLS))

unsigned int mandelbrot(double x, double y)
{
  double cx = x, cy = y, tmp;

  for (int i = 0; i < 1000; ++i)
  {
    tmp = cx * cx - cy * cy + x;
    cy = 2 * cx * cy + y;
    cx = tmp;

    if (cx * cx * cy * cy > 1000000000)
      return 0;
  }

  return 1;
}

int main(void)
{
  double cx, cy = FROM_Y;

  for (int y = 0; y < ROWS; ++y)
  {
    cx = FROM_X;

    for (int x = 0; x < COLS; ++x)
    {
      unsigned int point = 
        mandelbrot(cx,cy) + (mandelbrot(cx,cy + STEP) * 2);   

      putchar(point == 3 ? ':' : (point == 2 ? '\'' : 
        (point == 1 ? '.' : ' ')));

      cx += STEP;
    }

    putchar('\n');

    cy -= 2 * STEP;
  }

  return 0;
}
```