Most everyone has heard about fractals, right? You’ve seen pretty pictures like the one above, you know it’s some weird complicated math thing, and maybe you’ve heard about how they’re infinitely complex and you can zoom in on them forever and keep finding new patterns. Perhaps you’ve even heard that lots of things in nature, like mountain ranges and rivers, exhibit fractal patterns.
But if you’re like most people, you have no idea about the math behind these things. Maybe you thought it must be really complicated and you could never understand it – or maybe you’ve just never had time to try. I knew almost nothing about it, myself, until yesterday.
I did a little research. I learned exactly what equations are responsible for the picture above.
And you know what? It’s not that bad.
No calculus. No trigonometry. Just basic algebra and some very basic geometry. I picked it up in less than an hour. If you understand high school math, you can understand fractals.
And with the true zeal of a convert, I’d love to show you. I think it’s incredibly cool that the electric-looking beast in that picture (known as the Mandelbrot Set) was spawned by a single, very simple equation. I want you to experience that coolness too.
So, here’s what I’m proposing: next week is Fractal Week. Over the course of four days, I’ll carefully explain, step by step, how to build the Mandelbrot Set mathematically. I’ll answer any questions you may have. (I’m a volunteer math tutor once a week, so I actually have some practice with this sort of thing.) And then on Friday, we’ll all congratulate ourselves on being Fractal Badasses.
I know my man Ben Trube will be down with this plan, since he’s been writing fractal programs like a boss for years now. (He’s even posted pictures of his work.)
But what about the rest of you? Are you willing to take the plunge? Who’s willing to try Fractal Week with me?
Let me know in the comments!
Awesome! If you want I can pass along coordinates for some of the more interesting zooms into the set. As for simplicity, you’re right. That’s one of the things I love about Fractals, how complex they can be despite how simple the equation or iterated algorithm is that generates them. I first started playing with these things in the 6th grade, and programming them in high school (Anyone who has the manual for the TI-83 has a program they can write to make a Sierpinski Triangle on their calculator).
Man, I hadn’t thought about Sierpinski Triangles in ages, but we did do those in high school. Good times, right there. That’s like the Triforce on crack.
I’d try to follow, and if it’s possible that I may understand, I’d love to learn about fractals.
However, I haven’t yet experienced much high school math- if it weren’t for the books I read, I wouldn’t even know what a fractal is. And when you say basic algebra, and basic geometry, I wonder if you mean the a+3=7 type stuff and the geometry where you get to play with the pretty coloured tiles.
Because that’s about the extent of my knowledge.
It gets a little more complicated than that, but we’ll start with fairly simple algebra and work our way up. Worth a shot, anyway, and we don’t lose anything by trying. 🙂 If you have any questions, don’t be afraid to ask.
I’ll give it a shot!
Also, just because this made me think a bit about themed weeks, and I’ve been having some issues with Java, do you think maybe you could also do a post or two about programming? (That is, if you’re interested in doing that, and also if you’re familiar with programming in java. SInce you’re trying to create an a.i. let’s hope you are familiar with java). I’m still on the basics, mostly, (Probably since I just started programming last tuesday and I can only get lessons on tuesdays, 2 hours long). I understand what all the different symbols idnicate to the computer, however when I try to get unity to output a simple line of dialogue it refuses.
Apparently I need to define a system variable before the computer can output the line. Can you help me out? (I’ll take notes and listen to all that you say).
I’ve done a lot of programming in C++ and VB.NET, but it’s been a long time since I’ve written any Java. (The AI is in C++ currently.) If you give me a specific question and some lines of code, though, I can try and help you out.
Now this is what I’m talking about!
Sweet action!! I actually have seen that before, although it’s been a long time. I wonder how they made it?
They used a program called Mandelbulber. You can find it on sourceforge. They said each frame took about 90 seconds to render, so this thing takes some real horsepower heh. I downloaded it anyways, but haven’t experimented much with it.
It sounds a little over my head, but I’ll give it a shot! 🙂
Woohoo! Fractal week!! 😀
Fractalize that stuff! Did I use fractal as a verb? maybe, all I know is I should be able to fractalize anything I want.
Don’t fractalize me, bro!
Hah, you watch yourself. Next thing you know you’ll see millions of tiny yous hanging out near you. I’m sure this is possible due to my understanding of physics and fractals.
I can’t argue with that, it’s SCIENCE!
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