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A list of patterns that, when repeated to fill the cells of a Rule 30 automaton, repeat themselves after finitely many time steps. Frans Faase, 2003. Archived from the Original on 2013-08-08; Paving Mosaic Fractal. Basic introduction to the pattern of Rule 30 from the perspective of a LOGO software expert Olivier Schmidt-Chevalier.
Solution: divide one of the tall cells so that the row gets one rowspan=1 cell (and don't mind the eventual loss of text-centering). Then kill the border between them. Don't forget to fill the cell with nothing ({}). This being the only solution that correctly preserves the cell height, matching that of the reference seven row table.
These images depict space-time diagrams, in which each row of pixels shows the cells of the automaton at a single point in time, with time increasing downwards. They start with an initial automaton state in which a single cell, the pixel in the center of the top row of pixels, is in state 1 and all other cells are 0.
From the right: Starting from the right, the clues that are to the right of the 6 clue must be accounted for. Starting from cell 15, count 3 cells for the 3 clue (to cell 13), then a space (12), then the 2 clue (10), then a space (9), then the 6 clue (3). From the 3rd cell, "backfill" 4 blocks, filling cells 3 through 6.
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If a cell is discovered where none of the 9 digits is allowed, then the algorithm leaves that cell blank and moves back to the previous cell. The value in that cell is then incremented by one. This is repeated until the allowed value in the last (81st) cell is discovered. The animation shows how a Sudoku is solved with this method.
For instance, in Rule 90, a one-dimensional elementary cellular automaton, the population size starting from a single live cell follows Gould's sequence, which has a self-similar sawtooth pattern. On each step whose number is a power of two, the population crashes from a high of the step number plus one to a low of only two live cells.
2017/11/9 Origin 2018. Cell formula, Unicode, Bridge chart, changed to a more compact file format (OPJU). 2016/11/10 Origin 2017. Trellis Plot, Geology fill patterns, JavaScript support from Origin C. 2015/10/23 Origin 2016. First version to support Apps in Origin, also added R support.