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07:12am 09/11/2007
Julia Set fractal
Contemplating the fact that simple equations like zn+1=zn2+c can produce the infinitely intricate geometries of a fractal can honestly fill me with a sense of blissfully superlative awe, more so than any church ever could.

The basic equation I cited above produces the Mandelbrot Set fractal, as well as the Julia set fractals. The Mandelbrot Set is essentially a map of Julia sets. If you would like to see a visual representation which dynamically and interactively demonstrates the relationship between Julia sets and the Mandelbrot Set, the program Fraqtive does a beautiful job. You would need Linux in order to run the Fraqtive program though, so...

...With a Linux LiveCD you can boot into a functional [and temporary] Linux desktop without having to actually install Linux on your computer. (If you like a particular version of Linux enough to want it on your computer permanently, you can always install it to your hard-drive from a LiveCD.) The GoblinX LiveCD happens to have the Fraqtive program on it, so if you download the .ISO file for GoblinX and burn it to a CD you can then reboot your computer with the LiveCD in the drive and it will boot you into GoblinX (as long as your computer's BIOS is currently set to boot from CD prior to hard-drive, which is a setting that you can change). (The MD5 checksum to verify the fidelity of the downloaded GoblinX .ISO is 1d88aed9eb8e350e74dd301cf338f068.) Once you see the initial GoblinX screen, simply press the "Enter" key when prompted for a standard boot, and after logging in with the initial username and password that it supplies you, you select from one of the five possible desktops; I will recommend typing gof (and then pressing the "Enter" key) in order to select the FluxBox desktop (though any of the desktops should work). (The key combination of Ctrl+Alt+Backspace will exit from any Linux desktop and in GoblinX will take you back to the desktop selection screen.) Once the FluxBox desktop has booted-up, right-click on the desktop to produce the pop-up GoblinX Menu, and Fraqtive will be found under the Graphics submenu. (Coincidentally perhaps, the FluxBox desktop in GoblinX has a fractal background.)

Update: There are now versions of Fraqtive for Mac OS X and Windows, though I have never run the version for Windows so I cannot personally attest to its stability or performance on that platform.
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(no subject)
01:17am 11/11/2007 (UTC)
Seeing a still picture of a fractal is just not the same as exploring a fractal dynamically and interactively with a fractal generator program. With a generator program, it becomes a more personal experience.
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(no subject)
03:02am 13/11/2007 (UTC)
Whispered Symphony
I still remember that poster you had in your room in Fowlerville. I remember you explaining it to me a couple of times but most of the time I just thought the colors were really pretty. It does astound me that math(the subject I hate more than any other) can produce such beautiful and awe-inspiring images. Makes you realize there's more and more layers to the world. No matter how far you've dug.
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(no subject)
04:01am 13/11/2007 (UTC)
Mathematics, specifically in the form of Gödel's Incompleteness Theorems, guarantees that no matter how far you dig there will always be more layers.
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