## Census of small evolving patterns

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.

### Census of small evolving patterns

I have been thinking about ways to census small evolving patterns.
Here is an attempt:

Evolve them and check if they boil down into a single "small evolving pattern".
Consider it a "small evolving pattern" if the population is at most 12 on-cells in one generation and more than 12 on-cells in the next generation. After that the population must stay above 12 on-cells until it is "accepted".
A pattern is accepted on the generation when it has first reached a population of 20 on-cells or more, and after that has exhibited exactly 4 different population counts, all above 12 cells.

For example, this familiar pattern:

`x = 3, y = 3, rule = LifeHistory.2A\$2A\$.A!`

has the following population count in its evolution:

`Gen:  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22Pop:  5  6  7  9  8  9 12 11 18 11 11 10 13 16 19 19 23 25 35 25 32 27 37`

It goes from at most 12 cells to more than 12 cells from generation 7 to 8, but then drops down to 12 or lower again, so that's a false start.
Then it goes from 10 to 13 cells from generation 11 to 12.
It reaches 20 or more cells in generation 16, and in generation 21 it has had 4 unique population counts after that and is accepted.
Note that the population count is the same in generation 17 and 19, so it takes one extra generation before it's accepted.

Patterns are considered "the same" if they are identical in the generation they were accepted.
They can of course have reached that generation in many different ways.
The script picks one "small and common" predecessor of the accepted pattern to represent it (by keeping stastistics of common predecessors while collecting the accepted patterns).

I made a run of 10 million accepted patterns, which required 56 million soups to be tested.

Here's the most common 96 accepted patterns with the number of occurrences of each, and attached below is the full result of the most common 3980 small evolving patterns.

`x = 441, y = 1488, rule = 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The full result. As an example the switch engine is the second pattern from the left with 687 occurrences:
census.rle.gz

Source code:
tc.zip
simeks

Posts: 369
Joined: March 11th, 2015, 12:03 pm
Location: Sweden

### Re: Census of small evolving patterns

simeks wrote:Here's the most common 96 accepted patterns with the number of occurrences of each, and attached below is the full result of the most common 3980 small evolving patterns.

`x = 441, y = 1488, rule = 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Hmm...I imagine a database for the syntheses of these 96 would be useful in creating syntheses from soups.
Things to work on:
• Work on the snowflakes orthogonoid

Goldtiger997

Posts: 481
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E