https://github.com/mame/self-description-set

A formula that become itself when plotted
https://github.com/mame/self-description-set

Last synced: 16 days ago
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A formula that become itself when plotted

• Host: GitHub
• URL: https://github.com/mame/self-description-set
• Owner: mame
• Created: 2024-02-28T03:57:41.000Z (9 months ago)
• Default Branch: main
• Last Pushed: 2024-02-29T15:39:07.000Z (9 months ago)
• Last Synced: 2024-08-01T17:39:03.556Z (3 months ago)
• Language: Ruby
• Size: 73.2 KB
• Stars: 20
• Watchers: 2
• Forks: 1
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
![The self-description set](self-description-set.png)

---

THIS IS 〝THE SELF-DESCRIPTION SET $A$〟 WHERE:

$A = \lbrace (x, y) : x \in R \wedge y \in R \wedge (\lfloor x \rfloor, \lfloor y \rfloor) \in B \cup C \rbrace$

$B = \lbrace (x, y + 1) : x \in I(0, 240) \wedge y \in I(0, 59) \wedge g({\mathrm K}, 240 y + x, 2) = 1 \rbrace$

$C = \lbrace (x, -y - 1) : x \in I(0, 240) \wedge y \in I(0, 419) \wedge f(x, y) = 1 \rbrace$

$I(x, y) = \lbrace n \in Z : x \le n < y \rbrace$

$f(x, y) = g(g(2 {\mathrm F}, g({\mathrm K}, 4199 - 60 \lfloor \frac{y}{6} \rfloor - \lfloor \frac{x}{4} \rfloor, 10), 1048576), 4 {\mathrm mod}(y, 6) + {\mathrm mod}(x, 4), 2)$

$g(k, x, b) = {\mathrm mod}(\lfloor k b^{-x} \rfloor, b)$

${\mathrm F} = 731024063570851866511465264858993450227206304418681785374039$

${\mathrm K} =$

```

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```

---

```

$ ruby gen.rb > self-description-set.hs

$ runghc self-description-set.hs | ruby plot.rb

```

---

This was inspired by [Tupper's self-referential formula](https://en.wikipedia.org/wiki/Tupper%27s_self-referential_formula), made in 2009 [(Japanese article)](https://mametter.hatenablog.com/entry/20091106/p1).