7 in 7: Day 2 - Projective Geometry

Guiding Questions


I have been fascinated by emergent behavior resulting in beautiful patterns for some time now. I started back as an undergrad looking at Islamic geometric art and recall attempting to trace the methods of the old masters. Fractral geometry has been such a naturally recurring phenomenon that it has a spiritual status and can be seen on many spirituality websites.

Last night, I revisited this topic of interesting geometries, starting from more fractals (recursive geometry), to sandpile visualizations (cellular automata) to Petrie polygon projections (projection geometry).

The Idea

I’m trying not to use simulated methods involving code for prototyping, ruling out sandpile simulations and fractals. Rather I am curious about how to use strong sources of light to get rays to get light patterns. The idea was to arrange modules consisting of lasers with diffraction gratings around a circular track, such that the rays would intersect inside the circle to create patterns.


I first tried out using copper tape on my phone’s LED light source, since the blockage of lights would be more complete. I tried poking a hole through but the light is unfocused. I tried cutting a slit once using a pair of scissors, and it created a sort of diffraction pattern, which wasn’t what I wanted, though interesting to try this for myself.

I researched on how to focus light, and found out that no amount of optics on white light can create a fine ray, and the only way to do that is using lasers, essentially using electromagnetic waves of the same frequency.

Since I wanted to experiment with rays dispersing from a point, I needed some way to split it. I found that diffraction gratings do this, and that I can test this out using the plastic from CDs. This did not work out the way I expected. Either the CD was not cleaned of sticker coating enough, or the diffracted rays were too faint to be seen. I also tried seeing if crossing beams would cause the intersection to glow brighter.

I also experimented in making the laser rays more visible, in order to approximate the effect that I wanted. I tried spraying a water mist, and a finer spray from an aerosol. As the mist settled quickly, the ray was visible for only a short time.


There is something inherently fascinating in lasers, and more so when the paths are more defined. With the tools I had, I was not able to get a pattern, but the experiments gave me a better idea of working with lasers as a medium and how to make them more visible. I could build upon this and get (expensive) diffraction gratings which would give clearer paths, which would also be more coherent physics-wise. I could also get more laser diodes since they are inexpensive, and get enough to cause interference patterns. I would also need a smoke machine or dry ice or anything that generates finer, lighter particles to reflect the light.