Fractals Revived

[Aarondalf]

Not as funky as yours, but... well, I had a spare 20 minutes.

[MatthewV]

a page with all the "August" fractals. "August" has become a broad term. Means all the ones that are 08XX in my system. The first few are from this year, the last many are from last.

[One Skunk Todd]

The one in post 32 looks disturbingly like an open wound.

Anyway, you did do the sparkle one before, or at least something similar. It's been my wallpaper for a long time.

http://www.glpics.com/oneskunktodd/sparkle.jpg

[MatthewV]

A Rational render method

[MatthewV]

been busy. All the new pages are being updated.
sept, august, october



things might not be updated for a bit. try again in 1 hour if you have problems.

[MatthewV]

Mandelbrot with an orbit trap

[MatthewV]

been playing with the color set more. It looks like a scan of my brain...misfiring.
Mandelbrot set.


I believe the number of my fractals online has now reached 86.

[MatthewV]

Mandelbrot with an orbit trab. Looks like a shell to me.

[MatthewV]

Hmmm....a Rational fractal. mmmm

[MatthewV]

I will post another 277 fractals before this topic will die. I think.

From the Mandelbrot set.

[MatthewV]

Found in the orbit trap of the M-set.

[MatthewV]

Just like the last post...

[Dragon Phoenix]

Don't let it die! I love them!

[MatthewV]

oh, I said after 277 more didn't I? Do you know just how many 277 is??

[Aarondalf]

[Aarondalf]

[Jedo the Jedi]

Pardon my ignorance, but what exactly is a fractal, and how does it make those really, cool and mesmerising pictures?

*sits and stares at the things called fractals*
*sighs*

[MatthewV]

From memory and in laymans terms as much as possible...

1) A fractal is a mapping of an equation on the complex plain (real axis and imaginary axis). For every little tiny grid point, the complex numbers are plugged into an equation thousands of times. And then the number is determined to be "trapped" or "escaped". Trapped points are bounded inside the figure. Escaped points have a limit of infinity.
Because there are only two ture categories of "trapped" or "escaped" a graph of the image would only need black and white. This is not very pleasing to the eye, so for the escaped points a color value is assigned to how fast they escape. This value is found by the number of iterations it takes before it reaches a certain number that is know to escape.

2) It's a bunch of calculus that the computer does for your and makes pretty images.

[MatthewV]

Still dwelling in the orbit traps.

[Jedo the Jedi]

Thanks, MattV, that's rather interesting. Now, I think I'll go back to staring at these beautiful fractals. *sighs again*

[Bicho the Inhaler]

The term "fractal" was coined by Benoit Mandelbrot. He used the term more generally to refer to figures whose Hausdorff dimension is not equal to their topological dimension. "Huh?" you say? That more or less means shapes that are unusually "rough" and whose roughness does not disappear no matter how closely you look at them. The fractals MatthewV refers to are one particular kind.

One rule of thumb to tell if you're looking at a fractal is if it looks like it is made of smaller copies (or approximate copies) of itself.

These are really pretty, by the way

[MatthewV]

I should have done a tradition Mandelbrot set one here to show his point, but didn'.

From some complex rational equation...

[MatthewV]

Still in the Mandelbrot set.

[extropalopakettle]

[MatthewV]

The square version of the orbit trap, in the Mset

[One Skunk Todd]

Matthew and Aaron,
Do you have links to large versions of 812, 801, 704, 705, 709, and Quick2?

[groza528]

http://www.glpics.com/matthewv/largefractals/
Contains links to all of Matt's that you listed except 709.

[MatthewV]

yup, nearly every fractal is there. all but the one you see below I believe.

0709

using the "real" stalks in the orbit trab of the mset.


The problem with low quality appears to be coming from the jpeg method of compression. Fixed (I think), but grrrr.

[Aarondalf]

OST, actually no I dont have a large version of that. But I can try to make one similar to it. Shouldn't be that hard.

Mathew, was that last one rendered using anti aliasing? It looks like it could use it. Its all, edgy.

[MatthewV]

I fixed the problem that Arondalf sorry, I am proud of both of my t's :P posted. If you have a slow modem connection such as myself, you will notice that the picture loads in a slightly different fashion. Different types of jpg files. Strange.
you know, the difference between "mat" and "matt" is huge!
(most of the fractals should load top to bottom, this one does it "coarse to fine").

[Aarondalf]

LOL, Matthew. Mine was a typo, what's your excuse?



http://www.glpics.com/aaron/Cellular%20Fabrication_l.jpg

For some reason I really like that one.

[extro...]

[Aarondalf]

Orbit traps is a colouring algorithm.....

As for my one. If i recal correctly, it is a julia with a non zero seed value. The colouring algorithm is 'Triangle inequality average'

init:
float sum = 0.0
float sum2 = 0.0
float ac = cabs(#pixel)
float il = 1/log(@power)
float lp = log(log(@bailout)/2.0)
float az2 = 0.0
float lowbound = 0.0
float f = 0.0
BOOL first = true
loop:
sum2 = sum
IF (!first)
az2 = cabs(#z - #pixel)
lowbound = abs(az2 - ac)
sum = sum + ((cabs(#z) - lowbound) / (az2+ac - lowbound))
ELSE
first = false
ENDIF
final:
sum = sum / (#numiter)
sum2 = sum2 / (#numiter-1)
f = il*lp - il*log(log(cabs(#z)))
#index = sum2 + (sum-sum2) * (f+1)
default:
title = "Triangle Inequality Average"
helpfile = "Uf3.chm"
helptopic = "Html/coloring/standard/triangleinequalityaverage.html"
param power
caption = "Exponent"
default = 2.0
hint = "This should be set to match the exponent of the \
formula you are using. For Mandelbrot, this is 2."
endparam
param bailout
caption = "Bailout"
default = 1e20
min = 1
hint = "This should be set to match the bail-out value in \
the Formula tab. Use a very high value for good results."
endparam
}

[Aarondalf]

Oh yeah, and I zoomed in like a mother fucker

[Jedo the Jedi]

Wow! Post 67 and 70 are two of my favorites. Those are just gorgeous!

[MatthewV]

I unfortunately have no good explaination for what an orbit trap is. The purple lines in the fractal you mentioned are coming from this orbit trap. The method in this trap is "stalks" (real, imaginary or both.)

I am still using Fractal Domains (doing a google will work)

The Fractal Domains tell nothing about what an orbit trap really is or how they are generated. All it mentions is how to make them look nice and add flavor to a fractal image

[MatthewV]

Another Mandelbrot with an orbit trap.


A Julia based on the above image

[Aarondalf]

If you want i can show you the equation for orbit traps too.

Its really hard to know what an equation will "do", even if you have experience with the program or fractals in general.

[Aarondalf]

http://www.glpics.com/aaron/Nika_l.jpg

[Guest]

Aarondalf - are you using the same program? Windows or Mac?

I like the ones in post 54 and 55, and also that last one. Very "organic" looking, and different than what I've come to expect from years of poking around in mandelbrot and julia sets. I'd love to try doing animations based on those.

I posted this julia set animation some time back:
http://www.glpics.com/extropalopakettle/circ.mpg (1.7 meg)
http://www.glpics.com/extropalopakettle/circ.avi (.99 meg)

These were done with a trial version of some program (I can't recall), but the program only did stills. I wrote a java program to write input equation files for it, and had it produce a sequence of julia sets, each for a different point in the mandelbrot set. The sequence of points forms a circle near the mandelbrot set, so the animation loops - looks best if played continuously in a loop. Anyway, it would be neat to see those tree-like structures in posts 54 and 55, and that thing in the last post, animated.