2×2×9×9×16=5184

This artwork is made up of 5184 cells, in 72 rows and columns. The image represents all 1296 possible combinations of 3 core input variables within 2x2 square grid sections, from the system used to generate my path artworks. This same path system is also exhibited in my prior "Collage 001" NFT (ITEM #490) along with many other non-NFT artworks which I have previously shared online.

Each of these core input variables (denoted H, V, and C) are single-bit values (0 or 1) which govern the paths emerging from each cell. The 3 color channels (Red, Green, Blue) are mapped onto each of these bit values (C, H, and V respectively) such that a C/H/V value of 1 corresponds to a R/G/B value of 255. 8 of the 9 colors in this image result from that pattern. The final color, orange, is derived from more complicated multi-cell values which are explained further below.

In the path artworks themselves, each cell contains exactly 2 "path atoms". There are 23 unique path atoms, and 138 valid ways to pair 2 path atoms together. The path atom pair assigned to any single cell is defined by the 3 input bits at its own location, along with the input bits from 3 other neighboring cells (directly to the right, directly below, and diagonally to the right and below). Together this forms a 2x2 grid, the minimum space required to encode a given path atom pair. As a result of the rules governing cell-neighbor relationships, there are exactly 9 valid arrangements of "H bits" for a 2x2 grid. Similarly, there are exactly 9 valid arrangements of "V bits" for a 2x2 grid. The final "C bits" are governed less strictly, and can exhibit any of 16 valid arrangements within a 2x2 grid. The C bits are also unique in being partially derived from neighboring H and V bits, so not every combined arrangement of H and V allows for all 16 possible C bit arrangements.

These 5184 cells are arranged as 1296 2x2 squares, in 36 rows and columns. Each of these squares represents a set of 4 neighboring cells, whose 12 total input bits influence the resulting "path atom pair" displayed within its top-left cell. Within these 2x2 squares, each cell displays a color value derived from its unique position. The horizontal and vertical positions of these cells are directly analogous to horizontal and vertical positions of cells in the grids in my path artworks.

These 2x2 squares are arranged as 16 9x9 sections, in 4 rows and columns. Within these 9x9 sections, each 2x2 square displays a pattern of cell color values derived from its unique position. The horizontal position of a square within a section denotes the "H bits" (Green) of each cell, within this path artwork context, and the vertical position denotes the "V bits" (Blue). Each 9x9 section exhibits all 81 possible combinations of the H and V bits. Each of the 16 sections exhibits a different "C bit" (Red) arrangement, of the 16 total input possibilities for each 2x2 square. This C bit arrangement is held constant for all of the 2x2 squares within a given section, and only varies across sections.

The color palette of this project is based on a standard 8-color (3 channels, with 1 bit per channel) RGB palette, plus an additional ninth color of orange (239, 119, 24). Orange cells denote patterns in which the "chirality bit" (Red channel) has been demoted in value from 1 to 0. This demotion rule is itself a part of the rule system through which my path artworks are generated. Demotion of chirality impacts up to 43 specific cells within each of the sixteen 324-cell sections. This chirality demotion is a key component of ensuring that the "path atom pairs", assigned to each cell, yield continuous paths when connected to their neighbors in my path artworks.

This pattern of cell interactions (along with the rules governing the 3-bit color palette) has also previously been exhibited in 3 of my other NFTs (minted on HicEtNunc in 2021): "FNV-M-A", "FNV-M-ABC 001", and "FNV-M-ABC 002".

6310 by 6310 pixels, PNG, uncompressed. Generated in Python via the Pillow (PIL) library.