Math for VSFX

Updated on Feb 13  2017

also Houdini Resources


 Overview (pictoral)
 Overview (list)


copyright  Deborah R. Fowler



Phyllotactic Pattern

Deborah R. Fowler



Phyllotactic Pattern

Updated on June 22  2013
Updated with wrangles/lsystems on Sept 10  2016


   

   
    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.



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, 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).





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.
Exercise 1 VSFX350/721 will be implementing this in Houdini. Click here for some additional notes.
If you would like to see an implementation in