Tilings with Fractal Perimeters

Background

In a quest to represent the infinite by tiling a region with similar but smaller copies of a figure,
Escher's print Smaller and Smaller
Escher was inspired by Coxeter to produce his Circle Limit prints.
In these prints, circles are tessellated by similar (not in Euclidean geometry) figures that decrease in size but increase in number as they approach the circle.
Escher's print Circle Limit I
It may seem that this process should generate a fractal, but the limit set is the bounding circle, a completely Euclidean shape.
Peter Radeschelers and Robert Fathauer have made prints in a way mimicking Escher's approach, but with fractal perimeters.

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