Coding Math: Episode 35 - Intro to Fractals

[@EntangledFrequency]

exactly what I'm looking for. Very clearly explained and code is good.

[@israelRaizer]

Good to know the channel is back

[@danielm3977]

Pure beauty, I got a reward in high-school( more than 15 years ago), researching about Fractals and Chaos theory. Love it!

[@georgeshady1999]

Sick video . I thought I was the only one so fascinated with fractals

[@Polaroidon]

Yes! I've always had a huge interest in fractals, just never was able to figure out how to code them or anything fun. I really hope you put out a good number of minis on this like you said! Thanks as always!

[@Mishalka2013]

That's what I was looking for, great video. The way you produce fractals is absolutely easy, but was absolutely unseen to me before I watched it. I think almost everything works this way. I also have seen that some people describe fractal producing as transformations with matrices, which i think are nonlinear, now I think I understand this too and can code it.

[@simonmultiverse6349]

10:20 (approx) You're using trigonometric functions to compute angles. It would be easier if you used a 2x2 matrix to do rotation and shrinking, because this would be quicker than trigonometric and inverse-trigonometric functions. Also, a matrix will do the rotation and shrink _simultaneously_ . This would compute all fractals of this kind, i.e. fractals made of multiple smaller copies of themselves. IN ADDITION, you can make the matrix reflect, so some of the small copies of the whole could be reflected if you want.

[@sciboy123]

You can also draw the Sierpinski triangle very easily iteratively by plotting the orbit of a point. The process is as follows: take a random point p0 on the plane, set up the points of an equilateral triangle ABC. Pick one of the three triangle vertices randomly and move p0 halfway to that point (calculate its distance vector and divide by 2). If you repeat this process picking one of ABC randomly you eventually get Sierpinski s triangle.

[@rockysage7760]

Thanks man. Appreciate it. Exactly what I was looking for.

[@lucaug10]

That was fantastic, thank you for your videos. Really looking forward to more fractals.

[@rodrigod5625]

very good,I'm going to buy your book , it looks interesting :3 congratulations

[@tanmayg7824]

You can use the with(context){...} function to reduce the work!!

[@alexg4411]

OMG O_O so cool! Thanks! I would love to see more!

[@WeTheWounded]

"Is that a Fractal?" No. That is the Triforce.

[@leonli5067]

wow, this is really cool, thanks a lot.

[@mickyr171]

Could we consider the points between 1 and 0 to be a fractal? there are infinite many of them and they all begin with 0. so are self similar

[@oldjd7745]

Have you considered addressing a video on lacunarity

[@ReubenAStern]

Ok, I'm not working along with you, but this actually makes sense (Even though I wasn't taught trig, at school... guess I better learn it)

[@jontis96]

Very good video as always! But what's actually happening in the last sierpinski animation? Looks like it's rotating around it's Y-axis, whilst bending spacetime... I am assuming you are using some sinusoidal animation on pA, pB, pC?

[@KeithPeters]

yeah, you're pretty much spot on there. the code is in the github repo as always. github.com/bit101/codingmath

[@KeithPeters]

Basically, I just wondered what would happen if the mid points were not exactly half way, but some other percent. Then what if that percent was moving? Then, what if that percent were different on the x and y axes? I had no idea it would come out like that. Nice surprise.

[@redgray9801]

Wow! this is very nice topic one of my favorite FRACTALS. thank you for covering this too in coding math. I really like it. Am, are you planning to cover WebGL here too?

[@KeithPeters]

I'm really only planning on covering pure mathematical topics here, avoiding specialized libraries, frameworks, etc. I'm just using JS and Canvas because JS has kind of become the "lingua franca" of programming languages. But I wouldn't totally rule out doing something with WebGL some time in the future.

[@lucasmachain]

Keith I really admire you

[@theriffguy8237]

And it all began with a² + b² = c² and philosophically enshrined as, As Above, So Below. Later, As Within, So Without. Now. Fractals. Addendum: Euclid never put the 2, 3 or 4 on the Triangle, they were added. Pythagoras knew it too.

[@mikeseely5953]

i need that. book

[@bluestar-7]

amazing !!

[@ollllj]

pretty please do an example for "raymarching of signed distance fields that are defined by 3d-fractals" it can relatively easily be done in realtime in webgl, even with infinite reflections on surfaces that are close to the camera (or reflections that are still seen as being close enough to the camera) (and that have not too varying normals nearby to not distord the reflection too much). an opensource template for raymarching trough signed distance fields in webgl is github.com/nical/GLSL-Raymarching and you basically just define a 3d fractal deformation of a signed distance function to create a fractal 3d signed distance field. many youtube videos showcase results, but they are likely prerendered. with a few tweaks and loss of detail further from the camera it can be sone in realtime on hardware that is not younger than 2011, mostly because extended sse-like instructions for parallel processing were too bad for raymarching prior to 2007.

[@KeithPeters]

+ollj oh you know way more about this than I do. go for it! :)

[@coleraby]

+ollj oh you really should check out shadertoy.com, if you have not stumbled across that yet... e.g. check out www.shadertoy.com/view/XljSWK There are a huge amount of WebGL-examples to dive into and learn from.

[@coleraby]

+Keith Peters you might want to look into shadertoy.com too. One can really go insane with motion graphics there. Since I not always like having to mess around with the browser, I created a desktop variation of ShaderToy (launchpad.net/toyshader), which gives you a full OpenGL-environment, but allows one to take examples from ShaderToy and drop them into ToyShader almost 1:1.

[@coleraby]

+Keith Peters In terms of interactive fractals this will probably provide some fun... www.shadertoy.com/view/Xs3XWH (LMB-drag around the madelbrot-set :)

[@mutiaatika548]

what software you use to make this fractal??

[@LlewellynvonHellen]

JavaScript. He used JavaScript to make this fractal.

[@KeithPeters]

It's true.

[@jim0_o]

Very cool, what are some cool uses (except for being pretty to look at) ? I'm not saying it has to have more of a use, I'm just assuming this has one.

[@KeithPeters]

en.wikipedia.org/wiki/Fractal#Applications_in_technology Lots of uses in various fields of technology. As for everyday programming, useful in landscape/terrain generation or level design in games, or coming up with patterns that are not completely predictable, but not totally random either.

[@jim0_o]

Keith Peters nice, watching your Vimeo video at the moment, this stuff is pretty cool.

[@CIorox_BIeach]

I gave exactly 0 shits about coding until now.

[@ryanfuxa6738]

"Koch Snowflake"

[@satina1169]

can't I just use if else if else if else if else if else if else if else ... like yanderedev

[@davesmithSFCA]

*almost all math can be coded* _here is a sample of producing __#fractals__ in __#html5__ & __#javascript__..._