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# Rule 34

## Solution

Some pixels are mavericks.

Some pixels don't play by anyone else's rules.

Some pixels only want to watch the world burn.

**author: Satyarth Mishra Sharma**

So, if you look up rule 34 on google/wikipedia, you'll mostly see irrelevant stuff (hhhehehe). However, the wikipedia disambiguation page points you to elementary cellular automata.

If you look at the numbering system for elementary cellular automata, you'll get an idea of how an 8 bit number (0-255) can define 'rules' for the cellular automata. For example, rule 5 is 00000101 in binary, and all this is saying is "if the cells to the top-left, top, and top right of me are {111, 110, 101, 100, 011, 001}, then I'm a zero. Otherwise ({010, 000}), I'm a 1".

In this puzzle, you might notice a certain vertical periodicity. This might point you to try and find out the rules with which rows are generated. Here, every row is generated from the previous row by following a rule number. To find the rule for a row, you need to look at the eight possibilities for the pixels above it ({111,110,101,100,011,010,001,000}) and figure out the rule.

The clue tells you "some pixels don't follow the rules"- this is a reference to the light pink/dark blue pixels which indeed do not follow the rules of the rows that they are on. This was done to add a bit of randomness to the system- if we forgo this, the automaton can fizzle out quite quickly. So they still act as 1/0 for the row below them, but you can't use them to figure out the current row's rule.

Finding the rule numbers for the rows gives you a periodically repeating pattern of numbers, which when translated to ascii say "KappaKeepoDansGame".