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Aviar³
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 Posted: Wed Jun 06, 2012 10:23 am Post subject: |
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Well, beyond complex dynamics and particular fractals, are there uses?
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Cryoma
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| Posted: Wed Jun 06, 2012 10:34 am Post subject: |
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| Aviar³ wrote: | | Well, beyond complex dynamics and particular fractals, are there uses? |
Sure, biophysical math, since complex fractal patterns occur in the nature world, especially plant life.
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Aviar³
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| Posted: Wed Jun 06, 2012 10:36 am Post subject: |
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I can probably get decent 2D plant life using a simple L System. 3D plant life? Iunno, guess it might be useful then.
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Cryoma
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| Posted: Wed Jun 06, 2012 10:38 am Post subject: |
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| Aviar³ wrote: | | I can probably get decent 2D plant life using a simple L System. 3D plant life? Iunno, guess it might be useful then. |
Haha, that would be neat though, to have 3d fractal based randomly generated fauna in a game.
HINT HINT ZACKYPOO
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Slugsnack
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| Posted: Wed Jun 06, 2012 10:39 am Post subject: |
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| Cryoma wrote: | | Aviar³ wrote: | | Well, beyond complex dynamics and particular fractals, are there uses? |
Sure, biophysical math, since complex fractal patterns occur in the nature world, especially plant life. |
someone can't read 
| Cryoma wrote: | | Aviar³ wrote: | | I can probably get decent 2D plant life using a simple L System. 3D plant life? Iunno, guess it might be useful then. |
Haha, that would be neat though, to have 3d fractal based randomly generated fauna in a game.
HINT HINT ZACKYPOO |
this has been done already. also used to generate cities
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Evil_Intentions
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| Posted: Wed Jun 06, 2012 10:41 am Post subject: |
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| Aviar³ wrote: | | I can probably get decent 2D plant life using a simple L System. 3D plant life? Iunno, guess it might be useful then. |
No real need for complex numbers though in L systems, not even to model biological life.
I like them for their dynamics. Being that i is the square root of -1, and any complex number z = x +yi, squaring complex numbers gives interesting results:
Z = 3+2i
Z^2 = 3*3 + 6i + 6i + 4i^2
Z^2 = 9 +12i +4(-1)
Z^2 = 5+12i
What I've been trying to do is find ways to kind of fold complex numbers into L-Systems and see what the results would look like.
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Aviar³
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| Posted: Wed Jun 06, 2012 10:41 am Post subject: |
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| Cryoma wrote: | | Aviar³ wrote: | | I can probably get decent 2D plant life using a simple L System. 3D plant life? Iunno, guess it might be useful then. |
Haha, that would be neat though, to have 3d fractal based randomly generated fauna in a game.
HINT HINT ZACKYPOO |
Not a new concept, look at the Speedtree middleware (or is it API?) for games.
@Evil_Intentions: Didn't mean to make it seem like I was saying complex numbers are necessary ofr L-Systems (meant exactly the opposite). As to the particularities of imaginary numbers, I can't find any use for them beyond resolving negative roots. If you find anything interesting that you can do with it in terms of graphics please do tell.
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Cryoma
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| Posted: Wed Jun 06, 2012 10:47 am Post subject: |
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| Aviar³ wrote: | | Cryoma wrote: | | Aviar³ wrote: | | I can probably get decent 2D plant life using a simple L System. 3D plant life? Iunno, guess it might be useful then. |
Haha, that would be neat though, to have 3d fractal based randomly generated fauna in a game.
HINT HINT ZACKYPOO |
Not a new concept, look at the Speedtree middleware (or is it API?) for games. |
Speedtree isn't exactly what I had in mind, considering it's a rigid set of constraints with some variation.
What would be cool is to take an engine like speedtree but randomly generate those rule sets instead of prefabbing them, and doing that for each "biome" for lack of a better word, so you have all these varying wacky plants in different regions.
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Evil_Intentions
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| Posted: Wed Jun 06, 2012 10:48 am Post subject: |
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Yea, using fractal fauna is certainly not anything new.
@Aviar
Well graphically I'm looking at graphing L Systems normally in an X,Y grid but then treating them as if I graphed on the imaginary plane X,Yi. This makes any point in the fractal a complex number.
F+F-F-F+F starting at the origin yields
0+0i, 1+0i, 1+i, 2+i, 2+0i, 3+0i
I could then play around with this new bit of data, trying different methods of combining other complex numbers to contort the existing fractal into something new. Maybe something like multiplying them all by their conjugates to get real numbers, giving me:
0, 1, 2, 5, 4, 9
Then who knows what I could do from there, maybe something stupid as shit like making complex numbers from these
0+i, 1+2i, 2+5i, 5+4i, 4+9i
Or something to that effect. Now I could either graph these, or multiply them into the original fractal
So really I have nothing concrete yet, just some ideas to try out and play with to see how it effects some simple fractals.
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Cryoma
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| Posted: Wed Jun 06, 2012 10:55 am Post subject: |
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| Evil_Intentions wrote: | | Yea, using fractal fauna is certainly not anything new. |
It's new to me and google showed no results 
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Aviar³
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| Posted: Wed Jun 06, 2012 11:02 am Post subject: |
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| Evil_Intentions wrote: | Yea, using fractal fauna is certainly not anything new.
@Aviar
Well graphically I'm looking at graphing L Systems normally in an X,Y grid but then treating them as if I graphed on the imaginary plane X,Yi. This makes any point in the fractal a complex number.
F+F-F-F+F starting at the origin yields
0+0i, 1+0i, 1+i, 2+i, 2+0i, 3+0i
I could then play around with this new bit of data, trying different methods of combining other complex numbers to contort the existing fractal into something new. Maybe something like multiplying them all by their conjugates to get real numbers, giving me:
0, 1, 2, 5, 4, 9
Then who knows what I could do from there, maybe something stupid as shit like making complex numbers from these
0+i, 1+2i, 2+5i, 5+4i, 4+9i
Or something to that effect. Now I could either graph these, or multiply them into the original fractal
So really I have nothing concrete yet, just some ideas to try out and play with to see how it effects some simple fractals. |
As far as graphs and their geometric shapes go, I am pretty sure parametric equations give you more flexibility than standard functions on the cartesian plane, mostly since it lets you manipulate components (x, y, ,z) seperate of each other.
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