Thorn Fractal

This fractal is created by iterating the functions (x_n,y_n) and shading each pixel (x₀,y₀) depending on whether or how fast the series escapes to infinity. The parameter (c_x,c_y) is gives (slightly) different fractal images.

xn xn+1 = + cx cos(yn)

yn yn+1 = + cy sin(xn)

c_x = 0.102, c_y = -0.04

c_x = 1.098, c_y = 1.402

c_x = 9.984, c_y = 7.55

c_x = 0.662, c_y = 1.086

c_x = -0.354, c_y = 0.162

Movie example

c_x and c_y are moved around the unit circle, 1 degree steps.

Contribution by Dane Vandeputte

The following images were rendered virtually at 131072x81920 pixels (~10.7 gigapixels) and down-sampled on-the-fly using a properly dilated Lanczos3 filter. Colouring was applied using a simple lookup table approach based on linearly interpolated iteration counts in the escape time algorithm (bailout radius: 10000, maximum iterations: 500, (c_x, c_y) = (0.1, -0.1)). CLAHE (Contrast Limited Adaptive Histogram Equalization) was then applied multiple times with varying block size, threshold, and amount to enhance local contrast.