Nonlinear Iterated Function Systems 

Ordinary iterated function systems.  
Nonlinear functions are iterated in addition to affine transforms.
Log-density display instead of linear or binary (a form of tone mapping)
Color by structure (i.e. by the recursive path taken) instead of monochrome or by density.
The tone mapping and coloring are designed to display as much of the detail of the fractal as possible, which generally results in a more aesthetically pleasing image.[3][4]

Affine Transformations

The algorithm consists of two steps: creating a histogram and then rendering the histogram.
Creating the histogram

Density Estimation

 

Generalizations.

 

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