Quad pseudo still life

Quad pseudo still life[1] is the smallest pseudo still life that can be decomposed into four stable subpatterns (shown below), but cannot be decomposed into two or three stable subpatterns.[2] It was found by Gabriel Nivasch in July 2001. It consists of a single block surrounded by a hat, snake, and a 15-cell still life roughly made up of a snake and a hook with tail.

Quad pseudo still life
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View static image
Pattern type Pseudo still life
Number of cells 34
Bounding box 11×9
Discovered by Gabriel Nivasch
Year of discovery 2001

Uniqueness

Nathaniel Johnston showed on May 25, 2017 via an exhaustive computer search using Simon Ekström's still life searcher that there are no pseudo still lifes of 32 or fewer bits requiring a decomposition into 4 or more pieces,[3] and on April 5, 2019, he showed that there are no 33-bit pseudo still lifes with this property.[4] On January 9, 2020, he also showed that the quad pseudo still life is the unique 34-bit pseudo still life requiring a decomposition into 4 or more pieces.[5]

The first stable subpattern.
The second stable subpattern.
The third stable subpattern.
The fourth stable subpattern.
Catagolue: here
gollark: ``` ("D[dx, a#Num]", "0"), ("D[dx, a*b]", "D[dx, a] * b + D[dx, b] * a"), ("D[dx, a+b]", "D[dx, a] + D[dx, b]"), ("D[dx, dx]", "1")```
gollark: It's kind of hacky right now.
gollark: Yes.
gollark: I have implemented the "product rule" in my calculator.
gollark: Fear it.

See also

References
  1. Mark D. Niemiec (February 19, 2015). "29 Pseudo-still-lifes 26 bits and larger". Retrieved on April 3, 2016.
  2. Nivasch, Gabriel (July, 2001). "Still lifes". Retrieved on March 23, 2016.
  3. Nathaniel Johnston (May 25, 2017). Re: Enumerating Still Lifes (in C) (discussion thread) at the ConwayLife.com forums
  4. Nathaniel Johnston (April 5, 2019). Re: Enumerating Still Lifes (in C) (discussion thread) at the ConwayLife.com forums
  5. Nathaniel Johnston (January 9, 2020). Re: Enumerating Still Lifes (in C) (discussion thread) at the ConwayLife.com forums
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