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Lindenmayer System Squareflake

POpopswilson•Created November 14, 2012
Lindenmayer System Squareflake
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Instructions

Just click on the green flag and watch. The side of the original orange square are each an initiator. The first iteration draws the generator on each of the fours sides. The next iteration draws the generator, at a reduced scale, on each line segment of the the first iteration. And so on for the next iteration.

Description

See scripts for comments. The Squareflake has the amazing property that the area of the enclosed space never changes even though the perimeter grows without limit! Look at the first iteration and note the smaller square outside of the boundary on each of the four sides fits inside the boundary to show that there is no increase or decrease in the area! The Squareflake has a fractal dimension of 1.5, midway between a one-dimensional line and a two-dimensional area.

Project Details

Project ID2909658
CreatedNovember 14, 2012
Last ModifiedMay 30, 2016
SharedNovember 14, 2012
Visibilityvisible
CommentsAllowed