Medial Axes / Voronoi skeletons

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Holomorphic Functions

For a little more explanation of the mathematics of these functions of complex numbers, why I love them, and the architectural surfaces they can be used to generate, see my earlier post on rheotomic surfaces
Those coming from BoingBoing in search of Gnarl might also enjoy my 4D rotation animations or experiments with Cellular Automata.

 

Morphing Tessellation Fields 2

 

Morphing Tessellation Fields as Folding Patterns

My electric field sketch in Grasshopper controlling the metamorphosis of the MARS double corrugation pattern. Folded in Rigid Origami Simulator

 

Origami Electromagnetism

Andrew Hudson has been making some beautiful curved-fold origami using grids from my recent work with electric fields:

I’m really looking forward to seeing how this develops.

While we’re on the subject of origami…    (video)

I made this using Tomohiro Tachi‘s brilliant ‘Rigid Origami Simulator’ (He has some other great stuff on his Flickr)
You can see physical versions of the same corrugations in my earlier deployables vid.
Here are the patterns:

Numbers 3 and 6 were found in the 60s by Ron Resch.
I think number 4 was first done by John Mckeever and 2 and 5 by Ben Parker

The ‘bricklaying’ style number 2 in particular seems promising to explore further. It has a nice volumetric quality when fully folded and feels quite strong. It looks like it could be easily adjusted to give different curvatures.

I was thinking these corrugations might work well as the core in a (curved) structural sandwich panel. I wonder, is anybody already doing this sort of thing?

-update
just found an example of this sort of ‘industrial origami’ here: Tessellated Group

Next step would be to combine it with something a bit like this pattern for variable curvature (by Tomohiro Tachi again).

Of course you would need to fold the linerboard as well, or use multiple strips. But doubly curved sandwich panels – Surely that could be really useful for all sorts of things!

 

Jitterbug

download jitterbug.ghx

 

Cellular Automata Heightfield

In the best known example of Cellular Automata – Conway’s Game of Life, each cell has a binary state – it is either On or Off.
However, it is possible to explore similar automata where the state of each cell can be any real number in a given range – Continuous Cellular Automata.

The video above shows such a CCA in grasshopper. Each cell has a height value, which interacts with the values of its neighbours according to a simple* equation. This is a way of generating 3-Dimensional forms even though the cells only use a 2-dimensional Moore neighbourhood.

You can download the grasshopper definition here:
CAheights2.ghx

I made this by taking a Game of Life definition which Baldino had already made and simply copy-pasting some code from one of my earlier processing sketches into the VB component (well, I had to change a couple of bits of syntax, but surprisingly little).

The processing sketch uses colours instead of heights to show the value of each cell, and is mouse reactive:

Click image for Live Interactive version + sourcecode

Its strange the way it varies between periods of calm and chaos, without ever completely settling down or degenerating to noise.

* though it took me a fair bit of trial and error to come up with this particular equation. Just like the different rulesets explored by Wolfram, little changes can give quite different results, and I ran through all sorts of odd glitchiness before finding one I liked.