2022 Joint Mathematics Meetings
Nidhal Selmi
Artists
Statement
I'm Nidhal Selmi (@imleslahdin on twitter) By day, I'm just a software engineer. I was always inspired by fractals, impossible objects, isometric projections and cellular automata. In this work I merge those concepts together to generate an infinite universe of possible geometries. Special Thanks to Dr. John Baez (UCR) for shedding the light on the mathematics involving this work and motivating me to develop the generative program.
Artworks
Impossible structure using a 1-dimensional 4-state 7-cell-neighborhood cellular automaton.
Javascript
2019
Ten years after the impossible fractal, I had the idea of rendering it in an isometric projection using a 1D-7-cells-4-states Cellular Automaton. The automaton only requires less than a hundred rules if initialized with a simple seed to generate the original object from 2009, but the rules can be extended for different initialization to create intricate impossible structures. The rules do not always resolve to create a coherent, consistent object. In this case it took some manual care to pick the right rules that resolve the geometries in this example.
This is a fractal impossible object, packed with impossibility at multiple scales.
It's a blend of Sierpinski triangle, and Penrose tribar [1].
While the simple Penrose tribar only has one hole, this object -as we iterate further- has a countable infinity of them.
Penrose showed that his tribar gives a nontrivial element of first cohomology [2].
Dr. John Baez thinks that we can "work out the sheaf cohomology of the Sierpinski triangle and show Nidhal Selmi's impossible object gives an interesting element of the first cohomology!"[3]
[1] https://www.deviantart.com/nydhalo/art/Selmi-Triangle-136342456
[2] Penrose, R., 1992. On the cohomology of impossible figures. Leonardo, pp.245-247.
[3] https://math.ucr.edu/home/baez/diary/