Come here often and see all the crazy things that I have been upto!

Archive for January, 2012

FreakingAwesomeFractals

The day that I discovered fractals was the best day of my life! A fractal is an amazing phenomenon that happens when “an equation undergoes iteration, a form of feedback based on recursion,” according to Wikipedia (http://en.wikipedia.org/wiki/Mandelbrot_set). Let me show you the most “famous” (and in my opinion, insanely amazing) type of fractal, Behold the Mandelbrot Set, in all its glory!

Yeah, it might look a bit bland on the surface, but once you dig into it (yes, literally; ok fine, zoom in) and maybe even turn on colorcyling, you will have a sight handily beating whatever psychedelic drugs you think I’m on. The mysterious and miraculous formation of a fractal…

This little crazy thing called… oh right, a fractal! Upon closer inspection, you will observe that you can keep on zooming in for, well, pretty much forever! And the details only get more impressive yet bizarre as you zoom in, often with a peculiar self-similarity, like so.

Quite impressive with a small hint of creepy. Now I have never actually come up with my own fractal equations before, and don’t even ask me to explain how it works! I have no clue! But once I show you the complexity of the equation behind it, you will probably understand my confusion and utter lack of explanation.

M = \left\{c\in \mathbb C : \exists s\in \mathbb R, \forall n\in \mathbb N, |P_c^n(0)| \le s \right\}.

Yikes! Try parsing that one… is it a function? Now I know you’re probably thinking “ohh, he’s gonna go on and on about this topic that I really couldn’t care less about…”. Well that is true upto a certain point, but because you had the determination to read up until here, I have a reward in store for you. I want you to try out for yourself what instilled in me this passion for fractals. Why don’t I just give you a download link for software that will render colorful fractals for you!

http://www.chaospro.de/cpro40.exe

Yeah, there you have it, totally free and safe. Trust me, I have useeeeed it! I’ve probably already lost you to that oh-so-tempting download link by now, but anyways… maybe some instructions are a good idea, don’t get intimidated just yet!

First, install and launch the program (duh). Second, click File > Fractals > Escape Time to create your brand spanking new fractal.

To look around and amaze yourself, use your mouse’s scroll wheel to zoom in and out, and drag the view around to explore. It should look about like this.

May I suggest you start your own private party? Scroll down on the right sidebar to colorcycling and check that box, and let her rip! Your fractal should start pulsing all the delectable colors of a rainbow! Enjoy!!!

…Now if only my room had walls plastered with flatscreen tv’s outputting these in full 1080P glory! yessss, keep dreaming.

MathMineCraft

Minecraft is an amazing game, staged in a randomly generated world built utilizing 1 meter cubes. It is a type of sandbox game, in which you are free to do whatever you please. I use Minecraft to create epic feats of architecture, mostly large mansions or castles. One of my latest creations is a large, multi-floor brick mansion, with a large living room and balcony above it.

I wanted to have a curved, panoramic living room window, but because of the limitation of only square cubes, I had to improvise… somehow. I decided that the window should be parabolic, giving it an appealing and professional look. I tried building it on the spot, but couldn’t get it to look quite right… so I got an idea: Geogebra! I created a simple function based on the width and depth of the window, which ended up being:

I ended up with this graph, and placed a point on each full x integer on the parabola:

yeah, epic skills, ehh?

For each point on the graph, I placed a block that y-distance from the main wall. This made my window a perfect, uhm bumpy, parabola! Lovely perfection, with a mathematical formula behind it! Just the way I like it!

Well why don’t I show you the final product, and maybe give you the taste of playing Minecraft!