Dynamic Fractal Waves

[Kali]

I've been playing lately with the "dynamic fractal" concept first introduced by Tglad here at the forum, and I had the idea of applying this to sine waves used as displacement maps in distance estimated objects.

I had this Fragmentarium script I made some time ago, with a classic interference pattern between two wave generators:

<a href="https://dl.dropbox.com/s/tbu2jtscqkjmq2o/simplewaves.swf" target="_blank">https://dl.dropbox.com/s/tbu2jtscqkjmq2o/simplewaves.swf</a>


So I made some experiments based on this, but iterating the sin function and scaling frequency, amplitude, and propagation speed at each iteration.

This are the results so far:


POLES IN WATER

<a href="https://dl.dropbox.com/s/awvyogjlhk01t83/polesinwater.swf" target="_blank">https://dl.dropbox.com/s/awvyogjlhk01t83/polesinwater.swf</a>


SLIME SEA

<a href="https://dl.dropbox.com/s/tdw1xl2lz7wg8b4/slimesea.swf" target="_blank">https://dl.dropbox.com/s/tdw1xl2lz7wg8b4/slimesea.swf</a>


I used four wave generators in this one. It made me think of my attempt at the classic non-newtonian fluid experiment I made some years ago and uploaded to Youtube :

<a href="http://www.youtube.com/v/Hgd9Be7P3w4&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/Hgd9Be7P3w4&rel=1&fs=1&hd=1</a>


CHARLIE'S FACTORY

<a href="https://dl.dropbox.com/s/x3bq8a20qesypog/chocofactory.swf" target="_blank">https://dl.dropbox.com/s/x3bq8a20qesypog/chocofactory.swf</a>

Is fake, but it really looks like a falling flow of liquid chocolate . I used a torus on the waving plane with a cylinder inside, four wave generators placed at the torus border, and a central one...  I guess the faster moving waves on top of the slower ones simulates a laminar flow or something.


Then I tried with 3D waves, using radial space displacements. With the generators aligned on the 2D plane (at the same heigth), an interesting effect occurred:


SWAMP BUBBLES

<a href="https://dl.dropbox.com/s/341lfphmecmcqdx/bubbles.swf" target="_blank">https://dl.dropbox.com/s/341lfphmecmcqdx/bubbles.swf</a>



And the last one, using a 3D object:


LIQUID SPHERE

<a href="https://dl.dropbox.com/s/gbg7ndhs7onqnid/spherewave.swf" target="_blank">https://dl.dropbox.com/s/gbg7ndhs7onqnid/spherewave.swf</a>


I only used basic shapes for better showing the waves alone, but this can be used on any shape including fractals (I've already implemented a waving effect in some of the fractal animations I posted, but it was using simple sinewaves)

I'll be doing further research on this technique, and also I want to implement transparency/refraction for a better water effect (and making a perfect habitat for my underwater fractal creatures  )

Any comments appreciated.

[hobold]

There is a technique for generating fractal terrain that uses superposition of sine waves. It is called "spectral synthesis". I cannot easily find a good reference on the web. The method is described in "The Science of Fractal Images", edited by Peitgen & Saupe. Maybe you can find that book in a library. (I am unsure if I should recommend buying the book. It's good, but partly outdated by now.)

[KRAFTWERK]

You are about to create a new world Kali... Be careful, remember Frankenstein...

Great animations, and I love your experiment with non-newtonian fluid, it looks so alive. 

[Tglad]

Great work Kali, some high end ocean simulators use something similar  http://graphics.ucsd.edu/courses/rendering/2005/jdewall/tessendorf.pdf
Real oceans have been analysed and can be approximated by 'Phillip's spectrum' which defines how high the waves are for each wave length.
The paper then describes how you turn that spectrum into a set of sine waves at different frequencies, superimposed.

The dynamic fractal concept is probably a linear approximation of this spectrum. Though I think all waves should move at the same absolute speed for a proper 'conformal' dynamic fractal.

You can make simple waves (sine waves) into choppy waves by putting the horizontal position of each point also on a sine wave in the direction that the wave is travelling in.

[DarkBeam]

  sooo freaking cool

[cKleinhuis]

yeah some more to try out for the realtime section,
the poles in water look extraordinary real, and the fake chocolate as well has something, especially regarding the super low calculation time for this effect,
very nice to be used in games ....

so, you little crazy never stopping gpu coder implemented just the idea of tglad with the fractal animation ... awesome, is it true this has not been researched the slightes before ?!?!

awesome!!!

[cKleinhuis]

be sure to include the global illumintation code for out of the box caustics when playing with the water rendering

[eiffie]

There is a technique for generating fractal terrain that uses superposition of sine waves. It is called "spectral synthesis". I cannot easily find a good reference on the web. The method is described in "The Science of Fractal Images", edited by Peitgen & Saupe. Maybe you can find that book in a library. (I am unsure if I should recommend buying the book. It's good, but partly outdated by now.)

I didn't know it had a name! I had found the same trick and used it to make terrain, waves and clouds here:
http://www.fractalforums.com/landscapeterrain-generation/simple-non-standard-approaches/

[Kali]

First, thanks to all for the nice comments, and interesting/useful info.

@Tom: I tried with uniform speed, but it worked best for me when I scaled the speed twice: Speed*=(Scale*Scale). I'll post some examples later to compare.

@Johan: - There's nothing to worry about, except of my own mental sanity  

@Chris: Yes, next step is to implement that awesome renderer, if eiffie allows me to use his code  

@Hobold: Thanks, I'll try to find it, but it seems the same eiffie already did, and he also shared the code...  

@eiffie: Awesome stuff as usual, thanks for sharing (I didn't see it before).

@Luca: Not as cool as you  

@Kali: IT'S YOUR SON'S BIRTHDAY, GET OUT OF THE COMPUTER!!!

[Syntopia]

Great stuff, Kali - you really should try it with Eiffies new refractive GI shader.

[Kali]

Great stuff, Kali - you really should try it with Eiffies new refractive GI shader.

Thanks Mikael. I tried it, but my results are very noisy, I don't know if something is wrong or I must wait way a lot of subframes to render in order to get good results? if so, too slow for my patience   - also animation on progressive renderers is not working for me, or I don't know how to do it. Too bad because that GI looks so good  

But at least I managed to implement transparency/refraction on the good old "DE-Raytracer-v0.9.1". This renders pretty fast in realtime:


<a href="https://dl.dropbox.com/s/1dv58nty54qxifp/transparency_001.swf" target="_blank">https://dl.dropbox.com/s/1dv58nty54qxifp/transparency_001.swf</a>


I will share the script but first I must fix some minor issues.

Also I want to make the caustics, but I don't fully understand how it works yet...

[eiffie]

I only had patience for a fast render too
<a href="http://www.youtube.com/v/uQ&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/uQ&rel=1&fs=1&hd=1</a>

To get good caustics you need global illum (to pull in extra light rays) but you can fake it by counting the marching steps it takes to get thru the water's surface. If it doesn't take many steps lighten the object underneath. Of course I only thought of that AFTER I rendered. I had never placed one DE inside another - tricky! lol

But why isn't the octopus under there??

[Kali]

Nice video, eiffie!

I'll give a try at that cheap caustics, thanks.

The octopus is waiting for me to find a way to put him INTO the water. Yeah, tricky stuff indeed...

[Syntopia]

Thanks Mikael. I tried it, but my results are very noisy, I don't know if something is wrong or I must wait way a lot of subframes to render in order to get good results? if so, too slow for my patience   - also animation on progressive renderers is not working for me, or I don't know how to do it. Too bad because that GI looks so good  

Yep, GI is quite slow :-) As for the animation on progressive renders it should work after the latest fix - did you use the latest experimental binary in from the Non-DE thread? Otherwise please send me the code, and I'll take a look.

[eiffie]

I should have explained the fake caustics would be calculated on the number of SHADOW ray march steps. Not the primary ray. I did a version with the GI script with only 32 subframes for the water rendering and it looks pretty good:
<a href="http://www.youtube.com/v/CuHn9HdQQHE&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/CuHn9HdQQHE&rel=1&fs=1&hd=1</a>

I feel a little guilty about calling this GI since it doesn't really pull in that much light globally. More like "probabilty based path tracing". GI is just easier to say.