Tuesday, May 31, 2011

Complex Numbers

Ok, so, in the last few days I've learnt a few amazing things, and mostly these things are because of one person in particular, a certain fractalmath on youtube, who posted some videos a few years ago to explain how fractals are generated. He started by first explaining a bit about complex numbers, since they are an essential part of the fractal generating process. Thus, that is where I will begin too.

Please bare with me... It's all worth it in the end. After reading the next few posts, you will understand where the Mandelbrot Set comes from, but the process starts here.

Ok, so let's begin. You all remember the number line right? With all negative numbers to the left, positive to the right, and zero right between them? Something like this:
And you know that upon this line, all existing numbers can be found, whether they be huge, or tiny. 0.0000038885838943 can be found here, as well as 9,909,994,774,847,864,468 ... They're all there. And remember the term Real Numbers. Well all these guys on this particualr lin e are called exactly that: Real numbers.

Saturday, May 28, 2011

Introduction to Fractals

I created this blog with excitement, had fun with all the blogspot design settings, asked Mandelwerk for permission to intermittently use some of his work on the blog (he seemed happy with the idea, as long as I link back to him, of course), and got to work on the first post.

And then, as things usually go, all sorts of obstacles were thrown in my way, preventing me from continuing to learn about this sudden object of fascination. But at last, I'm back here.

So what now? Well, I'm taking this approach: I'm going to assume that whoever you are reading this, that you are in the same state I was when I started, i.e. that you know virtually nothing about fractals. You think they're cool; the result of mind-boggling mathematics-in-action and the source of some pretty amazing works of art, but that's about it.

So from here on out, I'll tell you exactly what I learn, as I learn it.

So what are fractals? It's all geometry. Just like a straight line, or a circle, fractals are geometric lines drawn on a physical plane too, but with more complex mathematical formulaes behind them. Let me try explain:

Take a straight line: You'll remember that, for example, "y=x" looks like this on the physical plane:

Easy enough right? And then if you change it a bit, the lines run differently: ...  

Thursday, May 26, 2011

In the beginning, there was ignorance...

Yes indeed, ignorance abounds... As of this moment, I know less about fractals and Mandelbrot/bulb than does your average teenage mollusc. But, I'm keeping my intimidation in check, starting this blog, and hoping for the best!

So if the above is true, how do I even know about fractals, you ask? Well, on a day in which I was feeling particularly lost as an expression-capable being, only truly able to come up with obscure forms of redundancy the like of this sentence, I stumbled upon the work of Mandelwerk, in Deviant Art. []

His beautiful fractal masterpieces intrigued me to the point of sudden obsession. I then continued to download his entire Gallery of work, base my entire W7 theme around them, join the fractalforums community, and start this blog.

Well, truth be told, the idea for the blog only came after a lot of (futile) searching for an easy, step-by-step tutorial on fractals, particularly Mandelbulb, and how to get creating my own vision of the same sort of Mandelwerk style I'd been bowled over by. (Because in the end, this is all about art.) To me, fractals are an incredible medium of artistic expression.

So after getting nowhere quickly, and especially after downloading the latest Mandelbulb program and feeling very, very silly indeed, I thought, "Hey, if you're going to dig deeper into this, since there doesn't seem to be anything of thelike around, you should start a Fractals for Beginner's blog, for all the future aspiring Fractalists who will come behind you."

And so, I did. Welcome! ... I hope you enjoy the journey with me.