Fun with Fractals

[Daddee]

Okay - here is a fun little program:Fractal Explorer 2.0. Go download it and use some of the tutorials that are linked to in the side bar of the main page (the link above is to the download page) to learn how to use it (this one is a particularly good list of them - but really, the operation is incredibly simple - nuance is complex, but the basics are really easy).

This is the coolest program. I've been fooling with it since it was just v. 1.24 - but the new 2.0 has good fixes for some of the annoying problems in v. 1.24.

Anyway - here are some of the images I've created (click on the thumbnail for the full version) - all of these images except one come from the primary fractal called a Mandelbrot set (the equasion for this image is just wild: Z=Fn1(Z); Z=Z*Z + Fn2(C) - not that it means anything to anyone, I just thought it was cool cause it's so simple - anyway - it is considered the most complex mathematical image we can generate)

This is what a Mandelbrot set looks like:


All of the following images were created by zooming in on that original graphic (some as much as 10,000x magnification):




These last images were created by altering the colors of the original set:


Or by using a different equasion - in this case a Newton attractor:


Now - go forth and create funky images.

Don't let the math fool you - to create these images involved no knowledge of the math - it is a graphics program first and foremost. If you understand the math you can do really cool stuff, but it isn't necessary.

Myself - I save the images I like into 1024 x 768 and use them as desktop graphics (all the large images that can be linked to are that size). If you're really into this type of stuff, you can get the 3-D generator as well and create fractal landscapes. That is pretty cool stuff - but I don't have quite the patience for it.
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"Only small minds want always to be right."
- Louis XIV

"...haven't you lived long enough to know that two men may honestly differ about a question and both be right?"
- Abraham Lincoln

[Tom Treks]

Wow. Grooovy dude!

It really would have done a number on Timothy Leary...

I'm still trying to figure out how it translates a mathematical equation into what you see.

[Daryl]

I keep trying to tell everyone that math is way cool. Maybe this will help!
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[Daddee]

I don't totally understand it all myself - but here is the best shot I can take at it:

We all worked with geometry in high school. In geometry you take an equasion and find a set of points that satisfy the equasion (for example: x2 + y2= 1). When you instead iterate an equasion instead of solving it, the equasion becomes a process instead of a description - dynamic instead of static. When a number goes into the equasion, a new number comes out; the new number goes in and on and on - points hop from place to place. A point is plotted not when it satisfies the equasion but when it produces a certain kind of behavior. One behavior might be a steady state, another might be a convergence to a periodic repetition of states, another might be an out-of-control race to infinity.

In the Mandelbrot set you simply take a number, multiply it by itself, and add the original number z = z2 + c

In the original post it looks longer because you have to label the function of 1 (Z) and function 2 (C).

Pretty wild. A 2 element equasion with only 4 characters results in the most complex mathematecal object.
_________________
"Only small minds want always to be right."
- Louis XIV

"...haven't you lived long enough to know that two men may honestly differ about a question and both be right?"
- Abraham Lincoln

[mike]

This new learning amazes me, Sir Daddee! Explain again how sheeps' bladders may be employed to prevent earthquakes.
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[/size]

[Daddee]

"And what else floats?"
"Small rocks!"
_________________
"Only small minds want always to be right."
- Louis XIV

"...haven't you lived long enough to know that two men may honestly differ about a question and both be right?"
- Abraham Lincoln

[ck1]

[Hikngrl]

My sentiments exactly Colin!
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~~~Diane~~~

I want to shine!

[Daryl]

Lets add calculus to the mix!
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[plummer150]

Crazy!
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"IRONMAN" cometh, hiketh, destroyeth

[kurthzone]

[kurthzone]

Anyone remember associate professor Babba Ramdas? (fried)
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;o)>

[Tom Treks]

Great tune. Moody Blues are cool.

Legend of a Mind

Timothy Leary's dead.
No, no, no, no, He's outside looking in.
Timothy Leary's dead.
No, no, no, no, He's outside looking in.
He'll fly his astral plane,
Takes you trips around the bay,
Brings you back the same day,
Timothy Leary. Timothy Leary.

Timothy Leary's dead.
No, no, no, no, He's outside looking in.
Timothy Leary's dead.
No, no, no, no, He's outside looking in.
He'll fly his astral plane,
Takes you trips around the bay,
Brings you back the same day,
Timothy Leary. Timothy Leary.

Along the coast you'll hear them boast
About a light they say that shines so clear.
So raise your glass, we'll drink a toast
To the little man who sells you thrills along the pier.

He'll take you up, he'll bring you down,
He'll plant your feet back firmly on the ground.
He flies so high, he swoops so low,
He knows exactly which way he's gonna go.
Timothy Leary. Timothy Leary.

He'll take you up, he'll bring you down,
He'll plant your feet back on the ground.
He'll fly so high, he'll swoop so low.
Timothy Leary.

He'll fly his astral plane.
He'll take you trips around the bay.
He'll bring you back the same day.
Timothy Leary. Timothy Leary.
Timothy Leary. Timothy Leary.
Timothy Leary.


Hmmm. Don't remember Babba Ramdas. What was his deal?