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Author Topic: Formulas  (Read 2362 times)
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scheven_architect
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« on: April 26, 2011, 11:44:59 PM »

Hello,

Is there a place where i can see what basic effect every formula has?

What formulas are most suitable if i wanted to create city/building like structures

What does julia do? I can't seem to find an answer that makes me understand.

Thanks in advance!

greetings!
« Last Edit: April 26, 2011, 11:46:55 PM by scheven_architect » Logged
DarkBeam
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Fragments of the fractal -like the tip of it


« Reply #1 on: April 27, 2011, 12:12:55 AM »

Your questions are too generic or unusual smiley ...
Julia mode is another way of computing escape time mandelbrot sets, that gives more regular and repeated shapes. a formula don't have a basic effect I don't know what you mean btw
Menger variants and ABoxes will help you to make buildings, I hope.
3da formulas are not affected by julia seed
good luck
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David Makin
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« Reply #2 on: April 27, 2011, 01:09:49 AM »

It sounds like you want stricter control over your creations than general escape-time formulas give you.
Apart from well-known/documented ones general escape-time formula results are often unpredictable and hard to control.
A fractal algorithmic method more suited to what you ask is probably "complete" IFS and in fact strictly affine IFS where you can pretty much predict exactly what you'll get from the transformations used especially if you stick to scaling, translation and rotations of multiples of 90 degrees.

For example the following where produced using my (escape-tiime) 3D IFS formula for Ultra Fractal in mmf4.ufm:

<a href="http://www.youtube.com/v/gKOIpe32BTE&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/gKOIpe32BTE&rel=1&fs=1&hd=1</a>
<a href="http://www.youtube.com/v/SnP4_OvKqxI&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/SnP4_OvKqxI&rel=1&fs=1&hd=1</a>
<a href="http://www.youtube.com/v/Fohy1-lqLxo&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/Fohy1-lqLxo&rel=1&fs=1&hd=1</a>
<a href="http://www.youtube.com/v/xNK8yNCXXx4&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/xNK8yNCXXx4&rel=1&fs=1&hd=1</a>
<a href="http://www.youtube.com/v/lFmCxPCmdFw&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/lFmCxPCmdFw&rel=1&fs=1&hd=1</a>
http://makinmagic.deviantart.com/art/Buddhist-Temple-89575614
http://makinmagic.deviantart.com/art/Sierpinski-Temple-detail-73751988
http://makinmagic.deviantart.com/art/Inside-the-Sierpinski-Temple-73257481
http://makinmagic.deviantart.com/art/Sierpinski-Towers-72857741
http://makinmagic.deviantart.com/art/Little-Boxes-69261153
http://makinmagic.deviantart.com/art/Menger-Homes-2-69784548
http://www.renderosity.com/mod/gallery/index.php?image_id=1578502&user_id=40328&page=2&member&np
http://www.renderosity.com/mod/gallery/index.php?image_id=1579019&user_id=40328&member&np

You'll note that these are essentially based on Sierpinski's and as Darkbeam said you can mix Sierpinskis/Mengers in with other formulas I think in both Mandelbulb3D and Mandelbulber but due to the nature of the formulas you mix them with results are often quite difficult to predict.

As to your question with respect to Julias at learstr in mathematical terms:

In general a Mandelbrot is actually a render of multiple functions of the form f(z)+c where the "c" is taken from the coordinates (screen coords. in 2D or virtual 3D+ coords in 3D+) where all iterations (normally) start with the same initial value of "z" before repeatedly applying z=f(z)+c for every pixel/voxel.
Julia Sets are renders of a single function f(z)+c because for Julias the value of "c" does not change, instead the coordinate value are used to give the starting value of "z" rather than the value of "c". So for Julia Sets every value of "c" gives a different Set.
Note however that for a Mandelbrot using f(z)+c with a fixed start value of z then every point on that Mandelbrot has a corresponding Julua Set associated with it where a single point in the Julia Set corresponds to a single point in the Mandelbrot i.e. where the initial z and the c values are the same.
I realise the above does not help much with respect to a general guide as to what shapes certain formulas may produce however the fact that each point on a Mandelbrot corresponnds to a point on a particular Julia actually gives interesting results from a geometric point of view - whatever the dimensiion of the fractal, if you have a given region on a Mandlbrot that produces geometry of interest then trying the Julia Set for the "c" values in that area of the Mandelbrot will almost certainly produce more of that kind of geometry.
Other than that knowing what formulas produce what structures is essentially more a thing learned through experience rather than descriptive guidance from others wink
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scheven_architect
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« Reply #3 on: April 27, 2011, 05:41:16 PM »

What exactly does julia (mode)? I'm sorry if this question is too generic, but I'm really new to fractals and nor the manual nor trying these xyzw values out seems to clear my mind :p.

Can i avoid the colored filling of my fractal when my camera is inside a fractal and 'slices' it?


greetings!
« Last Edit: April 27, 2011, 05:54:09 PM by scheven_architect » Logged
David Makin
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« Reply #4 on: April 28, 2011, 04:23:54 AM »

What exactly does julia (mode)? I'm sorry if this question is too generic, but I'm really new to fractals and nor the manual nor trying these xyzw values out seems to clear my mind :p.

Can i avoid the colored filling of my fractal when my camera is inside a fractal and 'slices' it?

greetings!

To understand Julia mode vs. Mandelbrot mode when new to fractals the best way is play around with a 2D fractal program and use that to get a personal understanding of exactly what the mathematical description I gave in my last reply means - that will help an awful lot when it comes to 3D+ fractals.

With respect to "solid" slices when inside a 3D+ fractal the short answer is no, the longer answer is it's possible but only if the rendering software you're using allows you to do so - it is possible to make the surface of a 3D+ fractal into a thin shell so it is a hollow structure - but rendering the "inside" of 3D fractals so it is transparent is notoriously difficult in the sense that it's very hard to get an algorithm to do so that is both fast and accurate.
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The meaning and purpose of life is to give life purpose and meaning.

http://www.fractalgallery.co.uk/
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DarkBeam
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Fragments of the fractal -like the tip of it


« Reply #5 on: April 28, 2011, 05:51:13 PM »

What exactly does julia (mode)? I'm sorry if this question is too generic, but I'm really new to fractals and nor the manual nor trying these xyzw values out seems to clear my mind :p.

Can i avoid the colored filling of my fractal when my camera is inside a fractal and 'slices' it?


greetings!

Okay but now Jesse made a point-n-click julia seed mode so no excuses, try it now evil grin
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