The Mandelbrot set

for each pixel (Px, Py) on the screen do
    x0 := scaled x coordinate of pixel (scaled to lie in the Mandelbrot X scale (-2.5, 1))
    y0 := scaled y coordinate of pixel (scaled to lie in the Mandelbrot Y scale (-1, 1))
    x := 0.0
    y := 0.0
    iteration := 0
    max_iteration := 40
    while (x*x + y*y ≤ 2*2 AND iteration < max_iteration) do
        xtemp := x*x - y*y + x0
        y := 2*x*y + y0
        x := xtemp
        iteration := iteration + 1

    color := palette[iteration]
    plot(Px, Py, color)

#include <SDL2/SDL.h>

#define WIDTH 800
#define HEIGHT 800

int main(int argc, char* args[]){

  SDL_Init(SDL_INIT_VIDEO);
  SDL_Window  *window  = SDL_CreateWindow("Mandelbrot set in c", SDL_WINDOWPOS_CENTERED, SDL_WINDOWPOS_CENTERED, WIDTH, HEIGHT, 0);
  SDL_Surface *winSurf = SDL_GetWindowSurface(window);
  Uint32      *pixels  = winSurf->pixels;
  SDL_Event    event;

  const int max_iter = 40;
  const float zoom = 2.5;
  const float colorFactor  = 256 / max_iter;
  const float widthFactor  = WIDTH / zoom;
  const float heightFactor = HEIGHT / zoom;
  float cr, ci, zr, zi, tmp;
  int x, y, iteration, color;

  // compute the set for every point
  for (x=0; x<WIDTH; x++) {
    for (y=0; y<HEIGHT/2; y++) {
      cr = x / widthFactor  - 2 ;
      ci = y / heightFactor - 1.25;
      zr = 0;
      zi = 0;

            // recurse
      for (iteration=0; iteration<max_iter; iteration++) {
        tmp = zr;
        zr = zr*zr - zi*zi + cr;
        zi = 2*tmp*zi  + ci;
        if ((zr*zr + zi*zi) >= 4) break;
      }

      // update the frame buffer
      color = (int)(iteration*colorFactor);
      pixels[x + y * WIDTH] = SDL_MapRGBA(winSurf->format, color, color, color, SDL_ALPHA_OPAQUE);
      pixels[x + (HEIGHT -1 - y) * WIDTH] = SDL_MapRGBA(winSurf->format, color, color, color, SDL_ALPHA_OPAQUE);
    }
  }

  // display the results
  SDL_UpdateWindowSurface(window);

  // wait for a key press
  while(SDL_TRUE)
    if (SDL_PollEvent(&event) && (event.type == SDL_QUIT || event.type == SDL_KEYDOWN)) break;
    else SDL_Delay(256);

  //releases the ressources and quit
  SDL_DestroyWindow(window);
  SDL_Quit();
  return 0;
}

#!/usr/bin/env python3

import math
import pygame
from pygame.locals import *

lenght=800
width=800

white = (255,255,255)
black = (0,0,0)

pygame.init()
gameDisplay=pygame.display.set_mode((lenght,width))
pygame.display.set_caption('Mandelbrot set in Python')
clock = pygame.time.Clock()
pixAr = pygame.PixelArray(gameDisplay)
gameDisplay.fill(black)

max_iter=40
zoom=2.5
colorFactor=255/max_iter
lengthFactor=lenght/zoom
widthFactor=width/zoom

for x in range(lenght):
    for y in range(int(width/2)):

        c = complex(((x/lengthFactor)-2), (y/(widthFactor)-1.25 ))
        z = 0.0j

        for i in range (max_iter):
            z = z*z+c
            if (z.real*z.real + z.imag*z.imag) >= 4:
                break;

        c = i*colorFactor
        pixAr[x][y] = (c,c,c)
        pixAr[x][width-1-y] = (c,c,c)

pygame.display.update()

while True:
    pygame.time.wait(10)
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            pygame.quit()
            quit()