An Experimental Gallery of Abstract Mathematical AI Art

Visualizing the Abstract

This work explores physical manifestations of some of the abstract mathematical ideas that I've pondered for many years. Fusing human creativity and artificial intelligence, made possible by recent advances in generative AI, I present metaphorical depictions of both the Rademacher average and the power mean. The Rademacher average gallery plays off the dual meaning of Rademacher as a German surname and a famous concept in probability, and the power-mean gallery references the ideas of social welfare, social justice, and the social planner in its design.

There's a lot I could say about this project, but good art speaks for itself. Let us see whether this art has anything to say.

The Rademacher Average

The Power Mean

Downloads

Full downloads of all images generated as part of these and other projects.

1. The Rademacher Average.
2. The Power Mean. Content Warning: minor female nudity. This seems to be an inevitability in AI generated classical art styles. I don't find any of these images to be sexual, exploitative, or offensive, and I wanted to release the complete set of uncurated images in addition to the above selection.
3. The Veil of Ignorance. Content Warning: moderate male and female nudity. Scenes depict various classical societies and contain somewhat explicit nudity. Again, I don't find any of these images to be sexual, exploitative, or offensive, but those who may should abstain from viewing them.
4. The Rawslian Game. These images were generated as part of this project.
5. Markov Clocks. This is a series of abstract visualizations of temporal dependencies within Markov chains. If I were feeling poetic, I might call them a meditation on the nature of time, sequentiality, and infinity.
6. Cats 2019 Movie Posters. I generated these posters for the (unintentional) gothic horror film Cats 2019. Perhaps the film wouldn't have been such a box-office bomb if the producers had possessed the foresight to hire me. As with all things Cats 2019, I do consider these images to be highly offensive.
7. Reflections of a Dream. An anthology of generatively illustrated haiku.

The Sudocube: An Experimental 3D Sudoku Puzzle

A puzzle by Cyrus Cousins

A 3D Sudoku puzzle, based on the number 2, rather than the number 3. Puzzle size is 4x4x4, with constraints along all three axes. Ideally, it would be 8x8x8, but for unknown reasons, nobody I asked wanted to pencil in 512 digits for an experiment puzzle. Basing it on 3 (as in a standard 3^2 x 3^2 puzzle) would have been far worse, with a puzzle size of 27^3 (i.e., 19683) cells, which just goes to show how quickly things can get out of hand with an extra dimension.

Domino constraints are given, but are not required to solve the puzzle. I have in my possession a solution key containing the unique solution, but I think I'll hang on to it; the puzzle is really more entertaining without.

This puzzle was created to encourage higher dimensional thinking, and to explore what changes when we generalize from the familiar to more abstract mathematical worlds.

Solve the Sudocube!

More Coming Soon!

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