Math for VSFX

Updated on March 1  2024

also Houdini Resources


 Overview (pictoral)


copyright © Deborah R. Fowler



Phyllotactic Pattern

Deborah R. Fowler



Phyllotactic Pattern

Updated on June 22  2013
Updated with wrangles/lsystems on Sept 10  2016
Updated with more examples on July 20  2018
Updated with vop versions on Jan 19  2019
Updated with OpenSCAD and blocksCAD versions on Feb 16  2020
Updated with new videos Jan 26, Feb 13  2021 and April 15, 2022






   

   
    Phyllotactic Patterns are a good start to using math for fun.
    There are a number of sites describing this pattern, including
    The Algorithmic Beauty of Plants, specifically Chapter 4 where I originally implemented this formula.



Other sites include:
http://www.math.smith.edu/phyllo//EXPO/ExpoIntro.html
http://www.mathsisfun.com/numbers/nature-golden-ratio-fibonacci.htm
http://demonstrations.wolfram.com/topic.html?topic=Plant+Biology&limit=20

Here is a brief description. Recently I have implemented this pattern in Houdini (multiple ways), C++/OpenGL, Python and Scratch as well as in the 90's with GL/C on Silicon Graphics Workstations (for those of you who remember what those are).

Polar to Cartesian video
https://vimeo.com/404190421






Now we have adj, which is our x coordinate and opp, which is our y coordinate, thus we have ( x, y )



Suppose now that
r, θ also are allowed to vary.



Where do these equations come from? Well from a paper by H Vogel 1979 in Mathematical Biosciences.
However, what this has done is reduced the problem to optimal packing on a disc.



 When we substitute these equations in for r and θ it results in the phyllotactic pattern.


Implementing this in Houdini or Python or  ...


So now you have the formulas, now what? You can use just about any graphics interface/programming language as a playground.
In class (VSFX350/721) you will be implementing this in Houdini. Click here for some additional notes.
If you would like to see an implementation in
See also the Zoetrope Phyllotactic Pattern- For more details click here.

    

Here are some more examples in Houdini using vex and various nodes. For more details click here.