Math for VSFX

Updated on Nov 25  2017

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copyright Deborah R. Fowler

Phyllotactic Zoetropes

Deborah R. Fowler

Phyllotactic Zoetropes

Posted on February 17  2015
Update on Sept 27  2015 to add WebGL version

A interesting video came to my attention about Fibonacci Zoetropes by John Edmark. Professor Edmark is an Art and Art History Professor at Stanford and his work was featured as a staff pick on vimeo. His website has many facscinating structures and it was his piece on Fibonacci Zoetropes that inspired me to try the 3-D CG version of phyllotaxis zoetropes. I have been familiar with spiral patterns since 1990, but had never tried a zoetrope. Thank you John Edmark for the inspiring idea.

The description of phyllotaxis from Chapter 4 of The Algorithmic Beauty of Plants (as described on my other page) follows the paper from Vogel in 1979:

Vogel, H (1979). "A better way to construct the sunflower head". Mathematical Biosciences 44 (44): 179189. doi:10.1016/0025-5564(79)90080-4

The model as it was described in 1979, produces the spiral pattern that is quite easy to implement in Houdini and has been used as an exercise in my procedural modeling and animation classes.

The changing size in "florets" has been more recently described in another interesting website. Kenneth Haugland posted code Sept 28, 2013 with an excellent formula for the size change as related to the pattern here.

Here is a phyllotactic zoetrope I created in Houdini.
Also here is my webgl version.

Related work:

The Siggraph 1992 paper describing phyllotactic patterns on surfaces of revolution can be found here.