The base animation for artwork submitted to the Fall 2015 Mission Arts Council / Prospera Credit Union local contest:
(The file is 20.8 MiB, so on slow connections, it may take a few minutes.)
The animation expresses mathematical and architectural ideas in a compelling and accessible way. The submission for the art show had some irrelevent embellishments in order to make the work 'artistic', and an altered title: 'Lifting Veils'.
My original motivation behind the artistic effort sought a generalized solution for multiply divergent phyllotaxis in two or more dimensions. The mathematics for that solution has been documented, but remains unpublished. Those with specific questions may contact me.
The practical motivation for the artistic effort was to use the mathematics to create patio or floor tile patterns using stock standard bricks and tiles. The animation depicts these patterns and their relationships for the geometric form of a standard metric construction brick.
Each frame is a tiling with n-fold divergence, where n is an integer greater than zero. My primary collaborative interest is in doing physical installations, so I am particularly interested in communications from those who would like to do something even as modest as a shower tiling.
The patterns are perhaps most suitable for public or institutional settings - a plaza or a lobby. The larger divergence multiplicities leave a hole in the center, which may variously accommodate a planter, a reception kiosk, a pond, a drain, or even an entire building, depending on the size implied by the divergence multiplicity.
It is also possible, but more difficult, to install such brickwork in a vertical wall. In that case the opening might be a window or door, highlighted by the brick pattern.
It is a simple matter to generate a list of precise positions and orientations, not only for the planar forms in the animation, but on curved surfaces, by adjusting a few parameters and running my code. I have also developed some practical methodologies for efficiently locating and laying physical tiles. The code that generates this data also remains unpublished. If you have interest in collaborating on an installation, contact me.
At some future time, after I have a few significant installations to my credit, I will publish the mathematics and the software so that others may freely imitate and perhaps expand upon my work.
It is of course possible to reverse engineer the pixel maps and obtain rough placement data, but why go to that devious trouble when the author of the ideas can provide you with data accurate to fifteen decimal places? Moreover, I can tailor a variation to your specific circumstance, using a multitude of alternate divergence angles or tile shapes. All you need to do is make a proposal for a collaboration.
For details, see: http://creativecommons.org/licenses/by-nc-sa/4.0/
The images in the animation are licensed under the Creative Commons version 4.0 CC-BY-NC-SA. That means you can explode the GIF and composite in a background photo of your puppy, or kitten, or girlfriend, or boyfriend, or whatever, but you may not sell such images commercially, and you may not use my artwork for commercial promotion of products without express written permission (and a commission). More tersely, you may make non-commercial derivatives, provided you assign credit to me for my artwork (the Creative Commons 'BY' clause). Such credit is most easily included by citing a link to this web page.