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Pythagorean tree:

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.

How to make dragon curve:

Ulam Spiral: all numbers from 1 to 100000; the more divisors a number has, the larger is the dot.

Comparison between 5,000 and 50,000 prime numbers plotted in polar coordinates

$\varphi$ curve:

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