Sierpinsky Triangle

Sierpinski-zoom4-aniThis is the Sierpinsky Triangle. Its generated by drawing a Triangle and then connecting the middle points of each side to form an upside down triangle. And repeat.

TypeIFS
Formula
ClassSponge
Hausdorff Dimension1.5849
Self-similarityidentical
ExamplesRomanesco Brocoli
Mountain Ranges
Some sea shells (e.g. Cymbiola innexa)
Discoverer

Generating a Sierpinsky Triangle by playing the “Chaos Game”

You can do the same for a square, which will give you the socalled Sierpinsky Carpet:
Animated_Sierpinski_carpet

There is also a 3 dimensional variant of this fractal, called the Menger Sponge:

Leave a Reply

Your email address will not be published. Required fields are marked *

Recent Posts