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Dr. Farnsworth entered class today and announced that we were going to conduct an experiment to see if we could force cells to evolve to communicate with us. The experiment is as follows: we are given a grid below, each containing a cell. As you can see, some of the cells are currently bioluminescing, while others are not. For each element of this cellular grid, we need to apply a single dose (1 gram) of Tungsten-102; because there are almost two hundred cells, we may wish to automate the procedure. Dr. Farnsworth claims that this application will evolve the cells, changing their luminescence to transmit a message to us. Can you help with this experiment, or is Dr. Farnsworth's time in the classroom numbered?

Cellular Grid

For those color-blind, the luminescing cells are colored bright green, and the non-luminescing cells are white. For those who will not want to transcribe the picture (i.e., everyone), an ASCII version is below, where 1 represents luminescing cells, and 0 represents non-luminescing cells.

101101000000001011000011110010110100000000101100101111001111010011110100110000000010110100101111001101001111111100101101001111001101000010110100110000101101001100001101001100001
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    $\begingroup$ Thank you for the ASCII version! $\endgroup$ – Deusovi Jun 10 '20 at 16:18
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What we need to do here:

Apply a 1-dimensional cellular automaton: that is, a rule that will "evolve the cells" based on their current state and their immediate neighbors.

More specifically:

"Tungsten-102" hints at using "rule 102" according to the Wolfram code. (Wolfram is the old name for tungsten.)

This produces the rule:
enter image description here

To read this table, for every cell you find the state of it and its immediate neighbors. The table tells you the new state. For example, the first entry says "if a cell is on and both of its neighbors are on, it turns off". The second column says "if a cell is on and only its left neighbor is on, it remains on". Together, the eight columns give you a rule for "evolving" the cells one step.

When this is done:


The new string is 1011100000001110100010001011101110000000111010111000101000111010001110101000000011101110111000101011101000000010111011101000101011100011101110101000111011101010001011101010001. (I've deleted the end cells, because their state is unclear; we could've had them wrap around, or treated their neighbors as always 0. Either way, the result is intelligible.)

This string turns out to be Morse code! In Morse, a dash is specified to be exactly three times the length of a dot, and we can see the 1s are all in groups of either one or three. Similarly, the intra-letter, intra-word, and inter-word spaces all match up.

Translating this, we get:

.-/-. . .--/-.- .. -. -../--- ..-./.--. ..- --.. --.. .-.. .. This decodes to give A NEW KIND OF PUZZLE!

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    $\begingroup$ Yeah, I figured this one wasn't going to last too long. You didn't explain all of my bad puns, but that's probably for the better :-) Awesome work! $\endgroup$ – Jeremy Dover Jun 10 '20 at 16:34
  • $\begingroup$ Additionally: the decoded message may refer to his book A New Kind of Science. $\endgroup$ – WhatsUp Jun 10 '20 at 18:09
  • $\begingroup$ @JeremyDover I am guessing another pun is that you suggest "automating" the process, i.e. using a rot13(pryyhyne nhgbzngba)? $\endgroup$ – htmlcoderexe Jun 11 '20 at 14:14
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    $\begingroup$ @htmlcoderexe: Yes. I wasn't sure how widespread knowledge of this topic would be in this forum, so I tried to include several prompts in the text. $\endgroup$ – Jeremy Dover Jun 11 '20 at 14:36

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