Click the cat to highlight 5 random cells, then click 3 more cells to try to make a valid pattern. Hover over the numbered buttons on the side to view the Miracle Octad Generator. To make valid patterns, take any of the grids from the Miracle Octad Generator, highlight all the cells of any two colors, and rearrange the three 2x4 bricks into any order. There will always be exactly one valid pattern which contains all five lit cells. --- Alternatively, find 8 cells that meet all three of these criteria: - Parity: The top row and each column must all have the same parity (the numbers of lit cells are all even or all odd). - Pattern: The hexacode of the grid (described below) must match one of these five patterns: 00 00 00; 00 aa aa; aa bb cc; 0a 0a bc; ab ab ab. The variables (a, b, c) each stand for a different non-zero digit, and each pair of digits may be flipped and the pairs can be rearranged. - Sign: There must be an even number of "negative" hexacode pairs present. These are: 10; 20; 30; 21; 32; 13. The hexacode of the grid is calculated by looking at the bottom three rows of each column and finding the only lit or only unlit cell among them. The rows correspond to the digits 1, 2, and 3 in order. If all or none of the rows are lit, the digit for that column is 0.
This is an explorer for the Miracle Octad Generator, a mathematical tool to help study the binary Golay code used in some error correction algorithms. Check out the YouTube video "The Most Powerful Diagram in Mathematics" by Another Roof for more information.
