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We're watching you $\require{action}\mathtip{{\Large \triangle}^{\hspace{-9.9pt}{{\bigcirc\hspace{-6.85pt}\odot}}}}{\text{Credits: Alexander Gruber}}$
Pythagorean tree:
![](https://cdn.statically.io/img/i.imgur.com/eFP73HR.gif)
For each natural number $n$, we draw a periodic curve starting from the origin, intersecting the $x$-axis at $n$ and its multiples. The prime numbers are those that have been intersected by only two curves: the prime number itself and one.
Below the currently highlighted number, we also show its sum of divisors $σ(n)$, and its aliquot sum $s(n) = σ(n) - n$, which indicate whether the number is prime, deficient, perfect or abundant.
![](https://cdn.statically.io/img/i.imgur.com/KsyylDr.jpg)
How to make dragon curve:
![](https://cdn.statically.io/img/28.media.tumblr.com/tumblr_m134rbjnYT1qbixhho1_400.gif)
Ulam Spiral: all numbers from 1 to 100000; the more divisors a number has, the larger is the dot.
![](https://cdn.statically.io/img/upload.wikimedia.org/wikipedia/commons/b/b0/Ulam_Spiral_Divisors_100000.png)
Comparison between 5,000 and 50,000 prime numbers plotted in polar coordinates
![](https://cdn.statically.io/img/i.imgur.com/dcaIVUZ.png)
$\varphi$ curve:
![](https://cdn.statically.io/img/i.imgur.com/pyUJR5e.gif)
![](https://cdn.statically.io/img/i.sstatic.net/y5Epq.gif)
![](https://cdn.statically.io/img/i.sstatic.net/AtDBi.gif)
![](https://cdn.statically.io/img/i.sstatic.net/QNydU.gif)
![](https://cdn.statically.io/img/i.sstatic.net/YonCw.gif)
![](https://cdn.statically.io/img/i.sstatic.net/Grvyq.gif)
![](https://cdn.statically.io/img/i.sstatic.net/7hrkV.gif)
![](https://cdn.statically.io/img/i.sstatic.net/QqedZ.gif)
![](https://cdn.statically.io/img/i.sstatic.net/KK6xx.gif)
![](https://cdn.statically.io/img/i.sstatic.net/zMDDO.gif)
![](https://cdn.statically.io/img/i.sstatic.net/XsK8s.gif)
![](https://cdn.statically.io/img/i.sstatic.net/eJur7.gif)
![](https://cdn.statically.io/img/i.sstatic.net/XU4CT.gif)
![](https://cdn.statically.io/img/i.sstatic.net/LbSLd.gif)
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