Growth Forms

George W. Hart

These are screen shots and video captures from a sculpture-generation project I am working on.
Click on each image to see an avi animation of it growing and tumbling.  (They are 15MB-70MB files.)

Start with an easy snakey thing.   (Click the image for the video.)

Simple radial growth

Coral-like structure (upwards branching growth only at tips)

Branching growth that also continues to grow everywhere

Four-limbed form

Octopus-like form

Pods with phylotaxis

Line growth, forming hyperbolic surface

Thing bearing fruit.  (See below for a physical model.)

A 12-limbed thing that is not icosahedral

Spiky guy

A thing that grows holes which pop through its surface and increase its genus.
It isn't  like any natural growth process I know, but there is something plausible about it.

Each form develops in real time from a small ball of cells by following a simple algorithm that is written in about a dozen lines of a "growth/form description language" which I am in the process of developing and implementing.  At every stage in the development, each form is a valid 3D object which can be built on a rapid prototyping machine. Details are available in this paper (which appeared in Bridges 2009).

For the topologically curious, these cells are colored by number of neighbors, corresponding to local curvature.

Here is a seven-inch plastic model (built by fused deposition modeling)
based on the stl file that is generated for an example above.

For fun, I painted it to match the above rendering, which helps bring out its cellular structure.