Mandelbrot Set

This is a simulation and rendering of the Mandelbrot Set, named after mathematician Benoit Mandelbrot, that provides a visual for the set of complex numbers that remain bounded in absolute value from the function.

The function is

f_{n+1} = f_{n}^2 + c

with the initial condition simply formed by taking the coordinates in the complex plane,

f_{0} = x + iy

It produces an aesthetic depiction of a fractal that does not diverge with recursive details similar in design to other parts of the fractal.

Code

Implementation

The programs were designed to simulate and render efficiently and each implemented unique high-performance optimization compilers. The namesake program was designed utilizing NUMBA AutoJIT high performance python compiler. The cuda extension was designed implementing parrallel computation with NVIDIA CUDA GPU technology.

Dynamic

@autojit
def create_fractal(min_x, max_x, min_y, max_y, image, iters):
  height = image.shape[0]
  width = image.shape[1]

  pixel_size_x = (max_x - min_x) / width
  pixel_size_y = (max_y - min_y) / height

  for x in range(width):
    real = min_x + x * pixel_size_x
    for y in range(height):
      imag = min_y + y * pixel_size_y 
      image[y, x] = mandel(real, imag, iters)

image = np.zeros((1024, 1536), dtype = np.uint8)
start = timer()
create_fractal(-2.0, 1.0, -1.0, 1.0, image, 20) 
dt = timer() - start

CUDA

@cuda.jit
def mandel_kernel(min_x, max_x, min_y, max_y, image, iters):
  height = image.shape[0]
  width = image.shape[1]

  pixel_size_x = (max_x - min_x) / width
  pixel_size_y = (max_y - min_y) / height

  startX, startY = cuda.grid(2)
  gridX = cuda.gridDim.x * cuda.blockDim.x;
  gridY = cuda.gridDim.y * cuda.blockDim.y;

  for x in range(startX, width, gridX):
    real = min_x + x * pixel_size_x
    for y in range(startY, height, gridY):
      imag = min_y + y * pixel_size_y 
      image[y, x] = mandel_gpu(real, imag, iters)

gimage = np.zeros((1024, 1536), dtype = np.uint8)
blockdim = (32, 8)
griddim = (32, 16)

start = timer()
d_image = cuda.to_device(gimage)
mandel_kernel[griddim, blockdim](-2.0, 1.0, -1.0, 1.0, d_image, 20) 
d_image.to_host()
dt = timer() - start

License

MIT

SVJayanthi / MandelbrotSet