From Sierpinski Triangle to Fractal Flowers

Anne M. Burns
Bridges Leeuwarden: Mathematics, Music, Art, Architecture, Culture (2008)
Pages 117–122


We describe an iterated function system consisting of transformations defined by a pair of complex parameters. Each of the transformations maps the unit circle into itself. For one assignment of the parameters the limit set is the famous Sierpinski Triangle. By “continuously” varying the parameters the limit set appears to erode into various shapes, some suggesting a dried river bed and others suggesting fractal flowers.