Mandelbrot set

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Generate and draw the Mandelbrot set.

C

Works with: gcc

This code assumes there exists a function DrawPixel taking as arguments the x and y position, followed by the red, green and blue components of the color. Note that this function is not part of standard C. <lang C>

define MAX_ITERATIONS 500

void draw(int width, int height){

 int x, y, colour;
 double x0, y0, xtemp, cr, ci;

 for (x = 0; x < width, x++){
   for (y = 0; y < height; y++){
     x0 = y0 = 0;
     cr = ((double)x / (double)width - 0.5);
     ci = ((double)y / (double)height - 0.5);
     i = 0;

     while (x0*x0 + y0*y0 <= 4.0 && i < MAX_ITERATIONS){
       xtemp = x0*x0 - y0*y0 + cr;
       y0 = 2*x0*0 + ci;
       x0 = xtemp;
       i++;
     }

     /* points in the set are coloured as white, others are coloured black. */
     colour = (i == MAX_ITERATIONS ? 255 : 0);

     DrawPixel(x, y, colour, colour, colour);
   }
 }

} </lang>

C++

This generic function assumes that the image can be accessed like a two-dimensional array of colors. It may be passed a true array (in which case the Mandelbrot set will simply be drawn into that array, which then might be saved as image file), or a class which maps the subscript operator to the pixel drawing routine of some graphics library. In the latter case, there must be functions get_first_dimension and get_second_dimension defined for that type, to be found by argument dependent lookup. The code provides those functions for built-in arrays. <lang cpp>

include <cstdlib>
include <complex>

// get dimensions for arrays teplate<typename ElementType, std::size_t dim1, std::size_t dim2>

std::size_t get_first_dimension(ElementType (&a)[dim1][dim2])

{

 return dim1;

}

teplate<typename ElementType, std::size_t dim1, std::size_t dim2>

std::size_t get_second_dimension(ElementType (&a)[dim1][dim2])

{

 return dim2;

}

template<typename ColorType, typename ImageType>

void draw_Mandelbrot(ImageType& image,                                       // where to draw the image
                     ColorType set_color, ColorType non_set_color,           // which colors to use for set/non-set points
                     double cxmin, double cxmax, double cymin, double cymax,  // the rectangle to draw in the complex plane
                     unsigned int max_iterations)                            // the maximum number of iterations

{

 std::size_t const ixsize = get_first_dimension(ImageType);
 std::size_t const iysize = get_first_dimension(ImageType);
 for (std::size_t ix = 0; ix < ixsize; ++ix)
   for (std::size_t iy = 0; iy < iysize; ++iy)
   {
     std::complex c(cxmin + ix/(ixsize-1.0)*(cxmax-cxmin), cymin + iy/(iysize-1.0)*(cymax-cymin));
     std::complex z = 0;
     unsigned int iterations = 0;

     while (iterations < max_iterations && std::norm(z) < 4.0) // note: std::norm(z) gives the *squared* absolute value of z
     {
       z = z*z + c;
       ++iterations;
     }

     if (iterations == max_iterations)
       image[ix][iy] = set_color;
     else
       image[ix][iy] = non_set_color;
   }

} </lang>