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Authors Alan Zucconi

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Alan Zucconi
Alan Zucconi
@AlanZucconi
Fifty years have passed since CONWAY'S GAME OF LIFE firstly appeared on a column called "Mathematical Games" on @sciam.

While most Programmers & Computer Science enthusiasts are familiar with it, not many know that the game is actually TURING COMPLETE.

Let's see why. โ  โ ต

๐Ÿงต๐Ÿ‘‡


The quickest way to prove that a system is TURING COMPLETE is to show that it allows for the constructions of LOGIC GATES. ๐Ÿ–ฅ๏ธ

So, let's see how the ๐—”๐—ก๐——, ๐—ข๐—ฅ and ๐—ก๐—ข๐—ง gates can actually be constructed in Conway's Game of Life...

Firstly, we need to find a way to encode binary signals.

One very popular choice is to use a stream of GLIDERS. The so-called GOSPER GLIDER GUN can generated a new glider every 30 generations. ๐Ÿ”ซ

Hence, receiving a glider every 30 generations counts as a "1".


When two GLIDERS hit each other in just the right way, they both get destroyed. ๐Ÿ’ฅ

This means that a GLIDER GUN can stop an incoming glider stream!

We can exploit this mechanism to simulate a NOT gate:

โฌ‡๏ธ ๐—ก๐—ข๐—ง 0 = 1 โฌ‡๏ธ ๐—ก๐—ข๐—ง 1 = 0


With the same principle, and AND gate can be also constructed by extending a NOT gate.

โฌ‡๏ธ 0 ๐—”๐—ก๐—— 1 = 0 โฌ‡๏ธ 1 ๐—”๐—ก๐—— 0 = 0
GAMING
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