Tglad
Fractal Molossus
Posts: 703


« on: December 01, 2010, 01:21:37 AM » 

Hello everyone, I was thinking yesterday how it would be really awesome to start animating 3d fractals like the KIFS in a fractal way. Currently animations vary parameters smoothly, what should look impressive is if they move so that the large pieces move slowly and widely, and the small details move quickly over small distances. Just like how a tree's trunk sways slowly but the small leaves flap quickly. If a reflection plane on a KIFS is given by a planePosition and planeNormal, then the code would be: float time = 0 for each animation frame { for each x,y,z { float t = time; vector v = (x,y,z); for each iteration { vector pos = planePosition + planeNormal*sin(t)*sizeOfMotion; v.reflectAroundPlane(pos, planeNormal); v *= scaleFactor; t *= scaleFactor; } } time = time + timeStep; // timeStep gives speed of motion } Jesse, Buddhi, Rrrola, would you be interested in trying this out?


« Last Edit: December 01, 2010, 01:23:22 AM by Tglad »

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The Rev
Guest


« Reply #1 on: December 01, 2010, 04:01:03 AM » 

This is a terrific idea. When I put together an animation, I have three dimensions (well, two actually) that are fractally generated, but the fourth is just how I choose to move the camera and/or fractal image around. It would be amazing to have four fractally generated dimensions, with movement being iterative in nature in line with the equation that generates the form.
The Rev



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Tglad
Fractal Molossus
Posts: 703


« Reply #2 on: December 04, 2010, 12:25:32 AM » 

Is anyone interested in trying this out? I promise I'll make some cool videos with it



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Tglad
Fractal Molossus
Posts: 703


« Reply #4 on: February 10, 2011, 02:09:23 AM » 

Here's another dynamic fractal:



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hobold
Fractal Bachius
Posts: 573


« Reply #6 on: February 11, 2011, 03:16:03 AM » 

The growing circles fractal is unique among the examples so far in that it is the only construction where the time axis is indeed interchangeable with the spatial axes. I'll try to explain this observation more clearly, so bear with me through what seems to be a detour.
Let's build a nonmoving fractal in three spatial dimensions. Specifically, let's take infinitely many filled spheres, the sizes of which adhere to a fractal distribution (i.e. few large ones, more medium sized ones and yet more small ones). We dither these spheres throughout space, nonoverlapping, with smaller spheres filling the gaps between larger spheres. Occasional void zones may exist, but these, too, are fractally distributed (i.e. few large gaps, but more smaller gaps and so on).
We now have a static sculpture of filled spheres in three dimensions.
Now choose one straight line through that sculpture of filled spheres. Move one point along that line at constant speed. Through the moving point, a cutting plane can be defined that is orthogonal to the straight trajectory of the moving point.
The cutting plane, when intersected with the three dimensional sculpture of static spheres, will display the growing circles fractal.
Another way to see this special quality of the growing circles fractal is the above construction backwards: take all animation frames and stack them on top of each other as slices of volume data. Some other examples will result in whipped cream, some in fractals with substantial directional bias, and only one example will result in an isotropic three dimensional fractal.



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jehovajah


« Reply #7 on: February 11, 2011, 09:57:46 AM » 

Super! Terrific! Fantastic! Glad i dropped by! In case nobody gets it, this is very important stuff!Its also way cool, too!



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May a trochoid of ¥h¶h iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!



Kali


« Reply #8 on: February 11, 2011, 02:29:28 PM » 

Tom, congratulations, another great finding. So simple ideas, so great results... this is what I love from fractals. (Also I think fractals are the answer to everything... a sacred plant showed me this, and this is the reason why I'm here at this forum)


« Last Edit: February 11, 2011, 03:53:50 PM by Kali »

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Tglad
Fractal Molossus
Posts: 703


« Reply #9 on: February 14, 2011, 05:56:39 AM » 

@hobold, you're describing a 3d cluster (or 3d fractals) viewed through a moving 2d slice, similar but not the same as the growth fractal. Moving slices can look interesting but they don't describe nature because time isn't a space dimension, it's separate. The dynamic fractals in this topic are still conformal, since we scale time by the same amount as distance. The next one is tricky:



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Kali


« Reply #10 on: February 14, 2011, 02:16:13 PM » 

Not even the greatest scientist or philosophers can describe exactly what really time is, so I wouldn't say for sure that it is a definite separated nonspatial dimension. Sorry about the offtopic, but check this out: http://en.wikipedia.org/wiki/Eternalism_%28philosophy_of_time%29



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Kali


« Reply #12 on: February 16, 2011, 12:38:34 AM » 

I don't see selfconectivity in the fractals of growing bubbles, neither in the orbits one.



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Kali


« Reply #14 on: February 19, 2011, 02:37:12 AM » 

@kali... what about being connected to its later or previous self?
Good point, but I find a little contradictory that you are pointing at that, after rejecting hobold's idea. It's pretty much the same. A 3D fractal made of stacking the 2D slices of each frame in the animation, is the best way to see this selfconnectivity you are talking about, don't you think? (temporal connectivity also suggest the idea of time being a spatial dimension) By the way, liked the Sierpinski dynamic fractal. Good work. One thing that has me thinking about the last dynamic fractals: As each self similar part of the fractal get's smaller, does it really moves faster? As for the treelike, the branches oscilates faster, but the distance between them it's smaller, so maybe the absolute speed of the edges of any branch it's the same? (or at least for the calculated median speed after a certain period of time, because they don't move at a constant speed) Also, in the Sierpinsky dynafractal, the smaller parts rotates at a faster rate, but as the radius is also smaller, maybe all the vertices have the same speed? I was also thinking what happens as we aproach infinity... infinite small parts oscilating or rotating at an infinite rate... It reminds me of something I read about string theory but I don't remember well what it was, I'll try to find it...


« Last Edit: February 19, 2011, 05:07:35 AM by Kali »

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