Fractal Ripples No. 3

The starting point for this graphically-constructed fractal is a group of concentric rings (a "ripple pattern"), with each larger ring being increasingly transparent. This ripple pattern is designed to mimic the waves that would form around a stone dropped in water. Four one-third-scale copies of the ripple pattern are positioned around the starting ripple pattern. The positions were intentionally chosen as the midpoints of the line segments in a Koch Curve construction. The resulting group of five ripple patterns is then scaled by one third, and four copies are positioned around the starting ripple pattern. This process is repeated until the new ripple patterns are so small as to be invisible to the eye at the scale of the print. Dark areas are created by the overlap of the waves, similar to constructive interference patterns. The final fractal reveals a Koch Curve, even though the ripple patterns are centered in what would be empty spaces in the curve. "Fractal Ripples No. 3" is a limited edition of 50 digital prints created in 2009; the image size is 15" x 10".

Copyright 2009 Robert Fathauer