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Here is a larger version produced using Fragmentarium (a free and open source shader editor).
It is actually downscaled from 10000x10000px to 2000x2000px using GIMP.

The formula used for this is:

z[0] = x + y*i, where x and y are the image coordinates

z[n+1] = i / ((a / z[n] - b/ z[n]) * e ^ (a / z[n] + b / z[n]))

where a and b are complex valued coefficients, controlling the behavior and structures of the result.

the color is generated by the HSL color space (converted to RGB) namely H = 0, S = 0, L = clamp(|z[250]|, 0, 1).