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content/posts/Tuppers-self-referential-formula.md

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@@ -10,21 +10,21 @@ I saw this old tweet today
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<blockquote class="twitter-tweet" data-media-max-width="560"><p lang="en" dir="ltr">Tupper&#39;s self-referential formula is a formula that visually represents itself when graphed at a specific location in the (x, y) plane. <a href="https://t.co/R0L3ZjqcyP">pic.twitter.com/R0L3ZjqcyP</a></p>&mdash; Fermat&#39;s Library (@fermatslibrary) <a href="https://twitter.com/fermatslibrary/status/1470392579288145931?ref_src=twsrc%5Etfw">December 13, 2021</a></blockquote> <script async src="https://platform.twitter.com/widgets.js" charset="utf-8"></script>
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The equation here is not the full picture. The "data" used to render this is contained within the constant `k` as seen in the plot. `k` is a 544 digit number that equals
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The equation here is not the full picture. The "data" used to render this is contained within the coordinate `k` as seen in the plot. `k` is a 544 digit number that equals
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```
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4858450636189713423582095962494202044581400587983244549483093085061934704708809928450644769865524364849997247024915119110411605739177407856919754326571855442057210445735883681829823754139634338225199452191651284348332905131193199953502413758765239264874613394906870130562295813219481113685339535565290850023875092856892694555974281546386510730049106723058933586052544096664351265349363643957125565695936815184334857605266940161251266951421550539554519153785457525756590740540157929001765967965480064427829131488548259914721248506352686630476300
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```
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Anyway, I wanted to see if I can plot this equation using matplotlib.
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<center>
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<br>
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$ \frac{1}{2} < \left\lfloor \text{mod} \left( \left\lfloor \frac{y}{17} \right\rfloor 2^{ -17 \left\lfloor x \right\rfloor - \text{mod} \left( \left\lfloor y \right\rfloor, 17 \right)}, 2 \right) \right\rfloor$
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<br>
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</center>
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discarding all the floors, we get
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discarding all the floors, we get
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<center>
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<br>
@@ -34,7 +34,7 @@ $ \frac{1}{2} < \text{mod} (\frac{y}{17} 2^{ -17 . x - \text{mod} ( y , 17)}, 2
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in python this would become
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```
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```python
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0.5 < ((y // 17) // (2 ** (17 * x + (y % 17)))) % 2
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```
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