Rule:DN-x4z

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@RULE DN-x4z

  1. By Yoel Matveyev, 2025
  2. A non-reflective version of Day & Night modified as follows:
  1. 0 0 1  ? ? ?
  2. 1 0 1 ==>  ? 1 ?
  3. 1 0 0  ? ? ?
  1. 1 1 0  ? ? ?
  2. 0 0 0 ==>  ? 1 ?
  3. 0 1 1  ? ? ?
  1. 1 0 0  ? ? ?
  2. 1 0 1 ==>  ? 0 ?
  3. 0 0 1  ? ? ?
  1. 0 1 1  ? ? ?
  2. 0 0 0 ==>  ? 0 ?
  3. 1 1 0  ? ? ?
  1. 0 0 1  ? ? ?
  2. 1 1 1 ==>  ? 0 ?
  3. 1 1 0  ? ? ?
  1. 1 1 0  ? ? ?
  2. 0 1 0 ==>  ? 0 ?
  3. 0 1 1  ? ? ?
  1. 1 0 0  ? ? ?
  2. 1 1 1 ==>  ? 1 ?
  3. 0 0 1  ? ? ?
  1. 0 1 1  ? ? ?
  2. 0 1 0 ==>  ? 1 ?
  3. 1 1 0  ? ? ?
  1. It has rotational symmetry, but lacks reflection symmetry. As this rule is declared anisotropic, one can tweak it any non-symmetrical way.

@COLORS 1 255 255 255 @TABLE n_states:2 neighborhood:Moore symmetries:none var A={0,1} var B=A var C=A var D=A var E=A var F=A var G=A var H=A

  1. Birth conditions

0,1,0,0,0,0,0,1,1,1 0,1,1,1,0,0,0,0,0,1 0,0,0,1,1,1,0,0,0,1 0,0,0,0,0,1,1,1,0,1 0,0,0,0,1,0,1,0,1,1 0,0,1,0,0,0,1,0,1,1 0,0,1,0,1,0,0,0,1,1 0,0,1,0,1,0,1,0,0,1 0,1,0,0,0,1,0,1,0,1 0,1,0,1,0,0,0,1,0,1 0,1,0,1,0,1,0,0,0,1 0,0,0,1,0,1,0,1,0,1 0,0,0,0,0,0,1,1,1,1 0,1,1,0,0,0,0,0,1,1 0,0,1,1,1,0,0,0,0,1 0,0,0,0,1,1,1,0,0,1 0,1,0,1,1,0,0,0,0,1 0,0,0,1,0,1,1,0,0,1 0,0,0,0,0,1,0,1,1,1 0,1,1,0,0,0,0,1,0,1 0,1,0,0,0,0,1,1,0,1 0,1,0,1,0,0,0,0,1,1 0,0,1,1,0,1,0,0,0,1 0,0,0,0,1,1,0,1,0,1 0,1,0,0,1,0,0,1,0,1 0,1,0,1,0,0,1,0,0,1 0,0,0,1,0,1,0,0,1,1 0,0,1,0,0,1,0,1,0,1 0,1,1,0,1,0,0,0,0,1 0,0,0,1,1,0,1,0,0,1 0,0,0,0,0,1,1,0,1,1 0,0,1,0,0,0,0,1,1,1 0,1,0,0,0,0,1,0,1,1 0,0,1,1,0,0,0,0,1,1 0,0,1,0,1,1,0,0,0,1 0,0,0,0,1,0,1,1,0,1 0,1,1,0,0,0,1,0,0,1 0,0,0,1,1,0,0,0,1,1 0,0,1,0,0,1,1,0,0,1 0,0,0,0,1,0,0,1,1,1 0,1,0,0,1,0,0,0,1,1 0,0,1,1,0,0,1,0,0,1 0,0,0,0,1,1,0,0,1,1 0,0,1,0,0,0,1,1,0,1 0,1,1,0,0,1,0,0,0,1 0,0,0,1,1,0,0,1,0,1 0,1,0,0,0,1,1,0,0,1 0,0,0,1,0,0,0,1,1,1 0,1,0,0,0,1,0,0,1,1 0,0,1,1,0,0,0,1,0,1 0,1,0,0,1,1,0,0,0,1 0,0,0,1,0,0,1,1,0,1 0,1,0,0,1,0,1,0,0,1 0,0,0,1,0,0,1,0,1,1 0,0,1,0,0,1,0,0,1,1 0,0,1,0,1,0,0,1,0,1

  1. Adding non-reflective B4z

0,1,0,0,1,1,0,0,1,1 0,0,1,1,0,0,1,1,0,1

0,1,1,1,1,1,1,0,0,1 0,0,0,1,1,1,1,1,1,1 0,1,1,0,0,1,1,1,1,1 0,1,1,1,1,0,0,1,1,1 0,1,0,0,1,1,1,1,1,1 0,1,1,1,0,0,1,1,1,1 0,1,1,1,1,1,0,0,1,1 0,0,1,1,1,1,1,1,0,1 0,1,0,1,1,1,1,1,0,1 0,1,0,1,0,1,1,1,1,1 0,1,1,1,0,1,0,1,1,1 0,1,1,1,1,1,0,1,0,1 0,0,1,0,1,1,1,1,1,1 0,1,1,0,1,0,1,1,1,1 0,1,1,1,1,0,1,0,1,1 0,0,1,1,1,1,1,0,1,1 0,0,1,1,1,0,1,1,1,1 0,1,1,0,1,1,1,0,1,1 0,1,1,1,1,0,1,1,0,1 0,1,0,1,1,1,1,0,1,1 0,0,1,1,0,1,1,1,1,1 0,1,1,0,1,1,0,1,1,1 0,1,0,1,1,0,1,1,1,1 0,1,1,1,0,1,1,0,1,1 0,0,1,1,1,1,0,1,1,1 0,1,1,0,1,1,1,1,0,1 0,1,0,1,1,1,0,1,1,1 0,1,1,1,0,1,1,1,0,1 0,1,0,1,1,1,1,1,1,1 0,1,1,1,0,1,1,1,1,1 0,1,1,1,1,1,0,1,1,1 0,1,1,1,1,1,1,1,0,1 0,0,1,1,1,1,1,1,1,1 0,1,1,0,1,1,1,1,1,1 0,1,1,1,1,0,1,1,1,1 0,1,1,1,1,1,1,0,1,1 0,1,1,1,1,1,1,1,1,1

  1. Survival conditions

1,1,0,0,0,0,0,1,1,1 1,1,1,1,0,0,0,0,0,1 1,0,0,1,1,1,0,0,0,1 1,0,0,0,0,1,1,1,0,1 1,0,0,0,1,0,1,0,1,1 1,0,1,0,0,0,1,0,1,1 1,0,1,0,1,0,0,0,1,1 1,0,1,0,1,0,1,0,0,1 1,1,0,0,0,1,0,1,0,1 1,1,0,1,0,0,0,1,0,1 1,1,0,1,0,1,0,0,0,1 1,0,0,1,0,1,0,1,0,1 1,0,0,0,0,0,1,1,1,1 1,1,1,0,0,0,0,0,1,1 1,0,1,1,1,0,0,0,0,1 1,0,0,0,1,1,1,0,0,1 1,1,0,1,1,0,0,0,0,1 1,0,0,1,0,1,1,0,0,1 1,0,0,0,0,1,0,1,1,1 1,1,1,0,0,0,0,1,0,1 1,1,0,0,0,0,1,1,0,1 1,1,0,1,0,0,0,0,1,1 1,0,1,1,0,1,0,0,0,1 1,0,0,0,1,1,0,1,0,1 1,1,0,0,1,0,0,1,0,1 1,1,0,1,0,0,1,0,0,1 1,0,0,1,0,1,0,0,1,1 1,0,1,0,0,1,0,1,0,1 1,1,1,0,1,0,0,0,0,1 1,0,0,1,1,0,1,0,0,1 1,0,0,0,0,1,1,0,1,1 1,0,1,0,0,0,0,1,1,1 1,1,0,0,0,0,1,0,1,1 1,0,1,1,0,0,0,0,1,1 1,0,1,0,1,1,0,0,0,1 1,0,0,0,1,0,1,1,0,1 1,1,1,0,0,0,1,0,0,1 1,0,0,1,1,0,0,0,1,1 1,0,1,0,0,1,1,0,0,1 1,0,0,0,1,0,0,1,1,1 1,1,0,0,1,0,0,0,1,1 1,0,1,1,0,0,1,0,0,1 1,0,0,0,1,1,0,0,1,1 1,0,1,0,0,0,1,1,0,1 1,1,1,0,0,1,0,0,0,1 1,0,0,1,1,0,0,1,0,1 1,1,0,0,0,1,1,0,0,1 1,0,0,1,0,0,0,1,1,1 1,1,0,0,0,1,0,0,1,1 1,0,1,1,0,0,0,1,0,1 1,1,0,0,1,1,0,0,0,1 1,0,0,1,0,0,1,1,0,1 1,1,0,0,1,0,1,0,0,1 1,0,0,1,0,0,1,0,1,1 1,0,1,0,0,1,0,0,1,1 1,0,1,0,1,0,0,1,0,1 1,1,1,1,1,0,0,0,0,1 1,0,0,1,1,1,1,0,0,1 1,0,0,0,0,1,1,1,1,1 1,1,1,0,0,0,0,1,1,1 1,1,0,0,0,0,1,1,1,1 1,1,1,1,0,0,0,0,1,1 1,0,1,1,1,1,0,0,0,1 1,0,0,0,1,1,1,1,0,1 1,0,1,0,1,0,1,0,1,1 1,1,0,1,0,1,0,1,0,1 1,0,1,1,0,0,0,1,1,1 1,1,1,0,1,1,0,0,0,1 1,0,0,1,1,0,1,1,0,1 1,1,0,0,0,1,1,0,1,1 1,0,1,1,0,1,0,1,0,1 1,1,0,0,1,1,0,1,0,1 1,1,0,1,0,0,1,1,0,1 1,1,0,1,0,1,0,0,1,1 1,0,0,1,0,1,0,1,1,1 1,1,1,0,0,1,0,1,0,1 1,1,0,1,1,0,0,1,0,1 1,1,0,1,0,1,1,0,0,1 1,1,1,0,1,0,0,1,0,1 1,1,0,1,1,0,1,0,0,1 1,0,0,1,0,1,1,0,1,1 1,0,1,0,0,1,0,1,1,1 1,1,0,1,0,0,1,0,1,1 1,0,1,1,0,1,0,0,1,1 1,0,1,0,1,1,0,1,0,1 1,1,0,0,1,0,1,1,0,1 1,0,1,1,1,0,0,0,1,1 1,0,1,0,1,1,1,0,0,1 1,0,0,0,1,0,1,1,1,1 1,1,1,0,0,0,1,0,1,1 1,0,1,0,0,0,1,1,1,1 1,1,1,0,1,0,0,0,1,1 1,0,1,1,1,0,1,0,0,1 1,0,0,0,1,1,1,0,1,1 1,1,0,0,1,0,0,1,1,1 1,1,1,1,0,0,1,0,0,1 1,0,0,1,1,1,0,0,1,1 1,0,1,0,0,1,1,1,0,1 1,1,1,1,0,1,0,0,0,1 1,0,0,1,1,1,0,1,0,1 1,1,0,0,0,1,1,1,0,1 1,1,0,1,0,0,0,1,1,1 1,1,0,0,0,1,0,1,1,1 1,1,1,1,0,0,0,1,0,1 1,1,0,1,1,1,0,0,0,1 1,0,0,1,0,1,1,1,0,1 1,1,0,0,1,1,1,0,0,1 1,0,0,1,0,0,1,1,1,1 1,1,1,0,0,1,0,0,1,1 1,0,1,1,1,0,0,1,0,1 1,1,0,1,1,0,0,0,1,1 1,0,1,1,0,1,1,0,0,1 1,0,0,0,1,1,0,1,1,1 1,1,1,0,0,0,1,1,0,1 1,1,1,0,1,0,1,0,0,1 1,0,0,1,1,0,1,0,1,1 1,0,1,0,0,1,1,0,1,1 1,0,1,0,1,0,0,1,1,1 1,1,0,0,1,0,1,0,1,1 1,0,1,1,0,0,1,0,1,1 1,0,1,0,1,1,0,0,1,1 1,0,1,0,1,0,1,1,0,1

  1. Making S4z non-reflective

1,1,1,0,0,1,1,0,0,1 1,0,0,1,1,0,0,1,1,1

1,1,1,1,1,1,1,0,0,1 1,0,0,1,1,1,1,1,1,1 1,1,1,0,0,1,1,1,1,1 1,1,1,1,1,0,0,1,1,1 1,1,0,0,1,1,1,1,1,1 1,1,1,1,0,0,1,1,1,1 1,1,1,1,1,1,0,0,1,1 1,0,1,1,1,1,1,1,0,1 1,1,0,1,1,1,1,1,0,1 1,1,0,1,0,1,1,1,1,1 1,1,1,1,0,1,0,1,1,1 1,1,1,1,1,1,0,1,0,1 1,0,1,0,1,1,1,1,1,1 1,1,1,0,1,0,1,1,1,1 1,1,1,1,1,0,1,0,1,1 1,0,1,1,1,1,1,0,1,1 1,0,1,1,1,0,1,1,1,1 1,1,1,0,1,1,1,0,1,1 1,1,1,1,1,0,1,1,0,1 1,1,0,1,1,1,1,0,1,1 1,0,1,1,0,1,1,1,1,1 1,1,1,0,1,1,0,1,1,1 1,1,0,1,1,0,1,1,1,1 1,1,1,1,0,1,1,0,1,1 1,0,1,1,1,1,0,1,1,1 1,1,1,0,1,1,1,1,0,1 1,1,0,1,1,1,0,1,1,1 1,1,1,1,0,1,1,1,0,1 1,1,0,1,1,1,1,1,1,1 1,1,1,1,0,1,1,1,1,1 1,1,1,1,1,1,0,1,1,1 1,1,1,1,1,1,1,1,0,1 1,0,1,1,1,1,1,1,1,1 1,1,1,0,1,1,1,1,1,1 1,1,1,1,1,0,1,1,1,1 1,1,1,1,1,1,1,0,1,1 1,1,1,1,1,1,1,1,1,1 1,A,B,C,D,E,F,G,H,0

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