Number of iterations:

Show both boards
  • Try these ``interesting'' designs: Squares, bridges, puzzle, caterpillar, scorpion, Decorative lattice, Jewels, Thue-Morse lattice, Spirals, swimmer, IFS: 1, 2, 3, 4,
  • You can navigate with keyboard (press "m" for movie etc).
  • Let me know ( if you find some other cool patterns that you'd like to add to the list.
  • Explanation: two boards are being assembled at the same time, call them left and right. For each iteration, a total of eight copies (some left, some right) are assembled after some transformations. These transformations are specified by placements and transformation rules. A transformation rule consists of eight digits, each digit must be from 0 to 7. Digit 0-3 means rotation by 0,90,180,270 degrees. Digit 4-7 means vertical flip followed by rotation of 0,90,180,270 degrees. These digits dictate how the eight individual pieces forming the two boards are being transformed. The first (last) four digits dictate how the left (right) board is formed. Placement is a sequence of eight zeros and ones, where zero represents the left board and one represents the right board. The four digits correspond to four pieces of the newly formed left board corresponding to upper-left, upper-right, lower-left and lower right corners, respectively. The last four digits is for the newly formed right board. The resulting rule is also shown graphically above. There is a total of 8^8*2^8=4.3 billion different rules, although some of them produce the same patterns.
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