Tuesday, November 07, 2006

Fractal trees

Initiators and Generators

One way to guarantee self-similarity is to build a shape by applying the same process over smaller and smaller scales. This idea can be realized with a process called initiators and generators.

The initiator is the starting shape.
The generator is a collection of scaled copies of the initiator.
The rule is this: in the generator, replace each copy of the initiator with a scaled copy of the generator (specifying orientations where necessary).


Here is the initiator of a binary fractal tree. The generator is a copy of the initiator with two smaller branches growing symmetrically from the top.

Changing the branching angle (and the branch scaling so the branches overlap only on their tips), gives a sequence of fractal trees, including a few familiar shapes.

Book bought:
-ดลใจภุมริน--รงค์ วงษ์สวรรค์

Book read:
-Anything--Edited by Cynthia C. Davidson

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