https://github.com/jbemmel/langton-ant-revisited

Revisiting Langton's Ant using Python
https://github.com/jbemmel/langton-ant-revisited

Last synced: about 1 month ago
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Revisiting Langton's Ant using Python

• Host: GitHub
• URL: https://github.com/jbemmel/langton-ant-revisited
• Owner: jbemmel
• License: apache-2.0
• Created: 2022-01-11T17:04:10.000Z (about 3 years ago)
• Default Branch: main
• Last Pushed: 2022-01-12T00:04:34.000Z (about 3 years ago)
• Last Synced: 2024-10-05T17:22:01.336Z (4 months ago)
• Language: Python
• Size: 29.3 KB
• Stars: 0
• Watchers: 4
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# Revisiting [Langton's Ant](https://en.wikipedia.org/wiki/Langton%27s_ant) using Python

In 1986 computer scientist Chris Langton came up with a way to illustrate the emergence of complex behavior out of a (seemingly) simple set of rules.

His article on ["Studying Artifical Life with Cellular Automata"](https://deepblue.lib.umich.edu/bitstream/2027.42/26022/1/0000093.pdf) describes the details.

![image](https://user-images.githubusercontent.com/2031627/149040592-ea2d20e3-533f-424e-a893-60ad88c94b03.png)

![image](https://user-images.githubusercontent.com/2031627/149033490-b0e5f63f-bdb8-483c-a483-51f72a15af3a.png)

# Data structures

The original algorithm uses a (bounded) 2D grid for the virtual ant ('vant'). In this implementation, it is replaced with a 1-dimensional array (implemented as a Python dictionary with integers as keys); directions (N)orth and (S)outh are implemented as increases/decreases of a fixed 'width'; it was found that a width of 48 is minimally required to keep the pattern from interfering with itself.

![image](https://user-images.githubusercontent.com/2031627/149033044-b217e17a-c746-43a9-b3ab-407cae59d653.png)

Sample 10 by 10 array; to go 'North' from 45, subtract 10

# Output: Repeating cycle of 104 steps

First occurence (104) after 10184 iterations, 14 loops highlighted

```

ESESWSENWNENESENWSWNWSENESESENWSWSWNESENWSWSESENWSWNESESENWSWSENWNESWSWSENWNWNENWNESWSESWSENWNENWNWNENES

    -----    ----- -----   ----  ----+++++   ----+++++ -----++++----- -----     -----   -----

```

N: 25

E: 27

S: 27

W: 25

Net displacement: 2*E, 2*S

Alternative RLE: Initial direction, then '1' for right turn or '0' for left turn:

```

10100111100100111100111100101111010000111101101111000010111101111000010111101001100001100111100110100100

     ----     ----  ----    ----  ----++++    ----++++  ---- ----++++  ----      ----    ----

```

(never 5 times in a row the same turn)

## Loop reduction

14 loops collapsed, removing 14*4=56 turns leaving 104-56=48

10100**1111**00100**1111**00**1111**0010**1111**01**00001111**0110**11110000**10**1111**0**11110000**10**1111**010011**0000**1100**1111**00110100100

```

10100111100100111100111100101111010000111101101111000010111101111000010111101001100001100111100110100100

101000010000001001011010010010011110000110100100

4 secondary loops, leaving 48-4*4=32:

10110010010110100100100110100100

```

```

ESESWSENWNENESENWSWNWSENESESENWSWSWNESENWSWSESENWSWNESESENWSWSENWNESWSWSENWNWNENWNESWSESWSENWNENWNWNENES

ESESWNENESWNESESWSWSESESWSWNWNENWSESWNENWNWNENES

ESENESESWSWSESESWSWNWNENWNWNENES

```

Impression of the resulting path:

```

                🡢   🡢

		 🡣 🡡 🡣

		  🡢🡢  🡢 

		   🡡🡣  🡣

		  🡢	🡠

		 🡡    🡣

		  🡠  🡠

		   🡡 🡣

		    🡠 🡢

	             🡡 🡣

		    🡢  🡢

		    🡡	 🡣

		     🡠  🡠

		      🡡 🡣

		       🡠

```