This is a collage of diagrams and charts, scanned from a selection of 25 pages of my notebooks. All of these notes relate to a generative art system which I have been building for the past several months. While developing the software for this system, I used (and continue to use) these tables and drawings to test rules before putting them into the code. Further explanation of the rules can be found in the final section of this description.
The hash functions used for data generation in the "digital version" of this algorithm have previously been exhibited in my "FNV-M-A", "FNV-M-ABC 001", and "FNV-M-ABC 002" artworks. While I have not yet minted NFTs of any other artworks from this project, I have exhibited a large variety of sample outputs on my Twitter throughout the past several months. For those interested in seeing outputs from the digital version, one such Twitter thread can be found here: https://twitter.com/mathMakesArt/status/1441560791468097536
The resolution of this piece is 5600 by 7700 pixels. The image file associated with this NFT is a compressed JPG (1.5 MB) in order to allow more reasonable load times, but you can download the full-quality PNG (35 MB) from my GitHub repository at: https://github.com/mathMakesArt/art/raw/main/collage-001.pn
The "arrow behavior" displayed in these diagrams is a 2-dimensional system for graphs with square grid connectivity. It can be applied to any rectangular grid section with side lengths greater than or equal to 3.
The behavior of a single arrow within any individual cell depends on 28 bits of information. Each individual grid cell receives 3 input bits, generated from its (x, y) position via the hash functions mentioned above. The arrow within any given cell depends not only on the input bits of its "parent cell", but also those of its 8 nearest "neighbor cells". These 9 cells each contribute 3 bits for a total of 27, and the remaining 1 bit corresponds to the arrow direction (horizontal or vertical). A majority of these 28-bit combinations are redundant and yield identical outputs to some other input; there are only 128 distinct states that any given unit cell can exhibit.