When you raise a complex number to p, with p being a list of numbers, and then proceed to add lines connecting them, why does it create these cool patterns?
That’s fun! Can you share a graph link?
Really, the pattern that I would make if the list was dense enough would be a circle/spiral inwards, but when you have a step on, it goes straight to different locations, causing a shape like this: Desmos | Graphing Calculator
yeah, it would be cool to make a spiral inwards forever but desmos still has the 10k list maximum.
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I believe this effect is due to De Moivre’s thereom (roots of unity). For example, repeatedly raising i to a power gives i->-1->-i->1->i. Complex numbers follow this formula:
(cos(x)+i*sin(x))^n=cos(nx)+i*sin(nx)
or more simply,
cis(x)^n=cis(nx)
(This is assuming the complex numbers have been converted to their respective trigonomic forms). You can find more information about this here: De Moivre's formula - Wikipedia.
If you divide @port’s list, p, it does become a more circular spiral.
there is a lot less variety that way though.
I like your original better, but was responding regarding the comment about a circular spiral.
i did not see that, my bad
I will find a way to bypass this
Also this is very cool
the key is emailing desmos asking for something
They won’t allow it, so I will just look in the source code and tell people how to modify it
ill try to look as well
The explanation lies in the fact that powers in complex numbers are like real powers but with a rotating angle:
this is the exact same algorithm that gives rise to sunflowers with a number of spirals given by a fibonacci number …
is there a way to imitate the patterns whilst not using complex numbers?