Pure Wrappings / Inflections

[hobold]

Pure Wrappings / Inflections



http://www.fractalforums.com/index.php?action=gallery;sa=view;id=20021

Toying with "inflections". As far as I understood them, they are really a wrapping of the complex plane around a given fixed center point. This can ultimately be expressed by a subtraction and a squaring of complex numbers.

In order to visualize a series of such wrappings, I started from a checkerboard pattern on the complex plane. But even when wrapped / inflected, this did not look all that interesting.

Then I layered a reciprocal (i.e. 1/z) on top of the checkerboard, which resulted in a nice, somewhat flower-like, center point around which the checkerboard gets smaller and smaller.

Finally the wrapping / inflection, when layered on top of the above, is nicely visible because it doubles the number of "flowers". So the eight "focal points" in this image are the result of just three wrappings / inflections.


Even without an underlying fractal formula, wrapping / inflection is a nice tool for producing interesting patterns.

[youhn]

Seems the property of period doubling of the embedded julia-shapes in the mandelbrot set can be seen as a more universal property. This is a nice development indeed!