Fern from a Chaos Game

Here’s an example of the chaos game played with four different maps based on four cases for a random number chosen between 0 and 1. The resulting attractor is known as the Barnsley Fern.

#chaos #chaosgame #fern #barnsleyfern #mathvideo​ #math​ #mtbos​ #manim​ #animation​ #theorem​​​ #iteachmath #mathematics #dynamicalsystems #iteratedfunctionsystem #dynamics #fractals

If you want to know more about the Chaos game, see the following links:

To learn more about animating with manim, check out:

[BlackDranzer-bfje]

Mathematics is really beautiful man ❤❤❤

[danaclass]

Saw this on Numberphile with Ben Sparks.. Absolutely incredible!

[salmonsushi]

mind blown please keep making these It reminded me of when i saw 3b1b short on polar prime point spirals

[mokhtarlahmer]

Beautiful the math and nature i think is the begining of understand the chaos theory

[hugominecraft]

I have made a simulation with your fracture ecuations and it has turned out really great, thanks; but I want to do this one yet I don't know what does the points represent, I mean, how to put them in a plane. Are they coordinates or something like that? Please answer. Thanks❤❤❤❤❤.

[adilkhatri]

universe is so mathematically organised.❤❤

[lumi]

question. how should one figure out the optimal probability distributions for IFS fractals, if one of the linear maps, like the stem in the barnsley fern, contracts the entire shape into a single line segment? by optimal distribution i mean, one that evenly distributes the points in a chaos game. i know that for fractals like the golden dragon, or the koch snowflake+interior, you can choose probabilities that are proportional to the absolute values of the determinants of the matrices, which are not the same for each map. but when one of the transformation has a determinant = 0, like in fractal trees and ferns, then how would one work it out? was the 0.01 for the stem chosen by feel? and what if one of the determinants is really close to, but not quite 0? how do you interpolate the method of finding the probability distribution between tiny and relatively large determinants?

[wcdeich]

I wish I could find a way to draw the solid outline of this fern.

[MichaelRothwell]

This is beautiful!

There's just one problem: you ask to choose r as a real number chosen randomly in the interval [0, 1] according to the uniform distribution.

But what kind of number could that be?

There's zero chance of it being rational. There's zero chance of it being algebraic. There's zero chance of it being describable.

So how would your random number generator communicate the number found?

Of course, if you only want the number to a given precision, there's no problem. But that's not very satisfying from a mathematical perspective.

[brano]

I do not understand. Can you point me to some additional information, some basis from which I can understand what is being referred to in the parentheses for X plus Y as well as R?

[AnglandAlamehnaSwedish]

The origin of between two ferns before Hollywood gots their hands on it

[qbanz]

But how and why ? No one can answer why

[oleksiyprosyanko]

What?! Write this. Why one number where coordinates are 2 numbers ?

[philroo]

Is this coincidence or is a fern running this algorithm?

[FundamSrijan]

Let's do this 35😊
Thousand times😮🤢🤮

[caspermadlener]

I see everyone talking about how beautiful mathematics is, but I think this is a little bit underputting the fine-tuning this person had to go though to make this.
Quite the example.

[thestra]

Nobody is going to be able to do this 35, 000 times

[exploreworldbirds]

Ferns demonstrates God's intelligence built into nature! 😊