Just a reminder all of this is sitting in this one little equation: \({Z}^{2}+C\)

@freemo \ x_{n+1} = r x_n(1 - x_n) \ is a simple enough population model. Lets try simulating it! Oh no...

@mandlebro @freemo

Did you know you can extend the bifurcation diagram for the logistic map

f: z → az(1-z)

beyond a=4 by solving

f^n(z) = z

for various n. The full picture is that for a>4 you get a repelling Cantor set!

@mandlebro @freemo it’s absolutely beautiful. I don’t understand it - but it’s beautiful 😁

@ErikaDesign It certainly is!

@mandlebro

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Refurio Anachro@RefurioAnachro@mastodon.cloud@mandlebro @freemo

Did you know you can extend the bifurcation diagram for the logistic map

f: z → az(1-z)

beyond a=4 by solving

f^n(z) = z

for various n. The full picture is that for a>4 you get a repelling Cantor set!