Chaos Game | Fractals emerging from chaos | Computer simulation |

I wanted to make a video about this topic for a long time, however without knowing how to code it would be really inefficient to animate every single dot by hand. So for the past few weeks I've been learning how to program animations and so I managed to simulate a chaos game.
Thanks for watching :)
_________________________________________________________________

Thank you everyone for 1000 subs. It's really cool that over a thousand people are actually interested in my content. I'm thankful for all the comments and support that I've been getting from you. I decided to create a Patreon page. If you feel like you would like to see more of my content as well as get to know more about me consider becoming a patron at :

_________________________________________________________________

Any further questions or ideas:

_________________________________________________________________

Overall render time: ~ 4 hours

Programs used:

- Processing (Game simulation)

- Cinema 4D (shape outline)

- Adobe Premiere Pro (Editing)

_________________________________________________________________

Music by: Tom Day

________________________________________________________________

[cinfdef]

Me putting a point directly in the center: *Reality can be whatever I want*

[kaninchengaming-inactive-]

The Legend of Fractal - Breath of the Chaos

[dubarnik]

Long time ago, I was an 8th grade math teacher. At the end of the year, after all the state testing was done and we were counting down days until summer break, I did a unit on fractals. I spent a couple of lessons teaching my students how to program their TI-83s to graph the Serpinski Triangle. The program is about 12 lines long and uses the algorithm at the start of this video. The program is still available and works on all of the TI-84s.

[ethangilchrist]

"Is this a fractal?"
"No, this is Patrick"

[Blananas]

"Oh, just random points, it can't be that intresti-- Wait what?"

[Tondadrd]

Cool,
A bit of research, putting the first point into proper position and it will become a rotation similar fractal. Right?
Btw. I came from *3b1b featured creators #1* and I'm happy I have. Your videos are showing pure beauty of math!

[FelineFlame-djxl]

I love how it pulls a 64 bits 32 bits 16 bits 8 bits 4 bits 2 BITS 1 BIT HALF BIT *QUARTER BIT* at 1:07

[marco_gallone]

I think “chaos” is interpreted incorrectly here, chaos essentially means *extremely sensitive to initial conditions*: change the initial randomly selected point marginally different from the first attempt and see a completely different pattern emerge. In this case it is more like “randomness”, and is opposite to chaos in that despite any random input conditions will always form a result with order.

[paramrathour]

You missed out on the fern one
Its really beautiful, a perfect fern just from chaos

[paithanq]

Why doesn't the last one have rotational symmetry?

[LittleFeet-eh]

We love you Think twice! Thank you for creating this iteration animation!

[tszheileung]

When you are just having fun with shapes but end up summoning a demon

[sparshsingh]

After all that I have learnt about fractals and their formation; (fixed initial condition and a fixed algorithm put on loop) the video title intrigued me beyond words. This concept further pushes us from our understanding of fractals.

[weakamna]

What you are describing here is an Iterative Function System, more specifically the "fractal flame algorithm", if you google that there is a paper as the second result. The first triangle algorithm you describe is the first one described in the paper. The paper goes on to describe techniques on how to improve the fidelity of the images generated (which can become very vivid and intricate!).

These are used by programs such as Apophysis(7x) or Fractorium (which is a gpu based implementation, which runs many many times faster on basically any computer with a graphics card). For people interested in this, I highly recommend reading the paper and then trying the programs out, maybe looking at more informal tutorials as well.

[jrtao]

why pentagon does not generate a symmetrical figure ? initial condition ?

[ineedtostudy]

I just woke up and I am not ready for this. I will come back when I am actually awake

[linsproul]

on the triangle, what if you put the first point in the center of the triangle? would that ruin the fractal?

[andistansbury]

2:20 I don't know what that fractal is called so I'm going to call it the serpenski rocket

[lucyluo]

your choice of music. Will be looking forward to hear your own music as background, would be cool ❤️

[giuseppepapari]

Nice! Have you tried to use an initial point that lies inside one of the empty areas in your fractal? What will happen? Will that be the only point outside the fractal? Or maybe the fractal only appears for certain initial points?