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Welcome to Fractal Forums > Fractal Software > 3D Fractal Generation > having troubles with 3D IFS
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Author Topic: having troubles with 3D IFS  (Read 2037 times)
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yoniHorn
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« on: July 05, 2010, 05:28:10 PM »
so i want to build a 3D IFS simulator.
i've already built an 2D ifs, and it's works great(download here: http://sites.google.com/site/yonisprogs/programs/IFS.rar)
and the 3D system is all set up , after i've built my 3D Function Drawer (download here: http://sites.google.com/site/yonisprogs/programs/3DFunctionDrawer.rar )

for those who are not new in IFS, i think i'll mange to produce a 3D IFS but for some reasons after some time of searching i can't find even 1 example of it! (I'm not talking about an image I'm talking about the functions!)
I'm looking for the Affine Transformations.

In 2D the Affine of the famous fern is:

w   a   b   c   d   e   f   p
ƒ1   0   0   0   0.16   0   0   0.01
ƒ2   0.85   0.04   −0.04   0.85   0   1.6   0.85
ƒ3   0.2   −0.26   0.23   0.22   0   1.6   0.07
ƒ4   −0.15   0.28   0.26   0.24   0   0.44   0.07

(source: http://en.wikipedia.org/wiki/Barnsley_fern)


I just need an example so i can start generation the IFSs.
thank you very much, Yoni.
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Timeroot
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« Reply #1 on: July 05, 2010, 06:00:10 PM »
Ahh, cool! I didn't read your source code, but I'm guessing you've only implemented affine transformations...  From what I know, I guess these follow something like

xNew=a*x+b*y+c*z+d;
yNew=e*x+f*y+g*z+h;
zNew=i*x+j*y+k*z+l;

Maybe something like Sierpinksi pyramid/tetrahedron would be good... I think that would be

w   a   b    c   d    e    f    g   h    i    j    k    l    p
f1 0.5 0.5 0.5  0  0.5 0.5 0.5  0  0.5 0.5 0.5  0 0.25
f2 0.5 0.5 0.5 .5  0.5 0.5 0.5  0  0.5 0.5 0.5  0 0.25
f3 0.5 0.5 0.5  0  0.5 0.5 0.5 .5  0.5 0.5 0.5  0 0.25
f4 0.5 0.5 0.5  0  0.5 0.5 0.5  0  0.5 0.5 0.5 .5 0.25

Note that this won't give you an *equliateral* Sierpinksi pyramid, more a sort of right-angled sierpinksi pyramid. Another simple formula. to make a Menger sponge:

w      a     b      c    d      e      f     g     h       i      j      k    l       p
f1   0.33 0.33 0.33   0    0.33 0.33 0.33   0    0.33 0.33 0.33  0    0.05
f2   0.33 0.33 0.33   0    0.33 0.33 0.33   0    0.33 0.33 0.33 0.33 0.05
f3   0.33 0.33 0.33   0    0.33 0.33 0.33 0.33  0.33 0.33 0.33  0    0.05
f4   0.33 0.33 0.33 0.33  0.33 0.33 0.33   0    0.33 0.33 0.33  0    0.05
f5   0.33 0.33 0.33   0    0.33 0.33 0.33   0    0.33 0.33 0.33 0.66 0.05
f6   0.33 0.33 0.33   0    0.33 0.33 0.33 0.66  0.33 0.33 0.33  0    0.05
f7   0.33 0.33 0.33 0.66  0.33 0.33 0.33   0    0.33 0.33 0.33  0    0.05
f8   0.33 0.33 0.33   0    0.33 0.33 0.33 0.66  0.33 0.33 0.33 0.66 0.05
f9   0.33 0.33 0.33 0.66  0.33 0.33 0.33   0    0.33 0.33 0.33 0.66 0.05
f10 0.33 0.33 0.33 0.66  0.33 0.33 0.33 0.66  0.33 0.33 0.33  0    0.05
f11 0.33 0.33 0.33   0    0.33 0.33 0.33 0.66  0.33 0.33 0.33 0.33 0.05
f12 0.33 0.33 0.33 0.66  0.33 0.33 0.33   0    0.33 0.33 0.33 0.33 0.05
f13 0.33 0.33 0.33 0.66  0.33 0.33 0.33 0.66  0.33 0.33 0.33 0.33 0.05
f14 0.33 0.33 0.33   0    0.33 0.33 0.33 0.33  0.33 0.33 0.33 0.66 0.05
f15 0.33 0.33 0.33 0.66  0.33 0.33 0.33 0.33  0.33 0.33 0.33 0.66 0.05
f16 0.33 0.33 0.33 0.66  0.33 0.33 0.33 0.33  0.33 0.33 0.33  0    0.05
f17 0.33 0.33 0.33 0.33  0.33 0.33 0.33   0    0.33 0.33 0.33 0.66 0.05
f18 0.33 0.33 0.33 0.33  0.33 0.33 0.33 0.66  0.33 0.33 0.33  0    0.05
f19 0.33 0.33 0.33 0.33  0.33 0.33 0.33 0.66  0.33 0.33 0.33 0.66 0.05
f20 0.33 0.33 0.33 0.66  0.33 0.33 0.33 0.66  0.33 0.33 0.33 0.66 0.05

Uh, yeah. I think that's it. I haven't tested it though. Happy fractaling!
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Someday, man will understand primary theory; how every aspect of our universe has come about. Then we will describe all of physics, build a complete understanding of genetic engineering, catalog all planets, and find intelligent life. And then we'll just puzzle over fractals for eternity.
cKleinhuis
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« Reply #2 on: July 05, 2010, 06:33:02 PM »
lol, i hope you wrote that numbers directly from your mind cheesy
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yoniHorn
Guest
« Reply #3 on: July 05, 2010, 07:31:21 PM »
Quote from: Timeroot on July 05, 2010, 06:00:10 PM
Ahh, cool! I didn't read your source code, but I'm guessing you've only implemented affine transformations...  From what I know, I guess these follow something like

xNew=a*x+b*y+c*z+d;
yNew=e*x+f*y+g*z+h;
zNew=i*x+j*y+k*z+l;

Maybe something like Sierpinksi pyramid/tetrahedron would be good... I think that would be

w   a   b    c   d    e    f    g   h    i    j    k    l    p
f1 0.5 0.5 0.5  0  0.5 0.5 0.5  0  0.5 0.5 0.5  0 0.25
f2 0.5 0.5 0.5 .5  0.5 0.5 0.5  0  0.5 0.5 0.5  0 0.25
f3 0.5 0.5 0.5  0  0.5 0.5 0.5 .5  0.5 0.5 0.5  0 0.25
f4 0.5 0.5 0.5  0  0.5 0.5 0.5  0  0.5 0.5 0.5 .5 0.25

Note that this won't give you an *equliateral* Sierpinksi pyramid, more a sort of right-angled sierpinksi pyramid. Another simple formula. to make a Menger sponge:

w      a     b      c    d      e      f     g     h       i      j      k    l       p
f1   0.33 0.33 0.33   0    0.33 0.33 0.33   0    0.33 0.33 0.33  0    0.05
f2   0.33 0.33 0.33   0    0.33 0.33 0.33   0    0.33 0.33 0.33 0.33 0.05
f3   0.33 0.33 0.33   0    0.33 0.33 0.33 0.33  0.33 0.33 0.33  0    0.05
f4   0.33 0.33 0.33 0.33  0.33 0.33 0.33   0    0.33 0.33 0.33  0    0.05
f5   0.33 0.33 0.33   0    0.33 0.33 0.33   0    0.33 0.33 0.33 0.66 0.05
f6   0.33 0.33 0.33   0    0.33 0.33 0.33 0.66  0.33 0.33 0.33  0    0.05
f7   0.33 0.33 0.33 0.66  0.33 0.33 0.33   0    0.33 0.33 0.33  0    0.05
f8   0.33 0.33 0.33   0    0.33 0.33 0.33 0.66  0.33 0.33 0.33 0.66 0.05
f9   0.33 0.33 0.33 0.66  0.33 0.33 0.33   0    0.33 0.33 0.33 0.66 0.05
f10 0.33 0.33 0.33 0.66  0.33 0.33 0.33 0.66  0.33 0.33 0.33  0    0.05
f11 0.33 0.33 0.33   0    0.33 0.33 0.33 0.66  0.33 0.33 0.33 0.33 0.05
f12 0.33 0.33 0.33 0.66  0.33 0.33 0.33   0    0.33 0.33 0.33 0.33 0.05
f13 0.33 0.33 0.33 0.66  0.33 0.33 0.33 0.66  0.33 0.33 0.33 0.33 0.05
f14 0.33 0.33 0.33   0    0.33 0.33 0.33 0.33  0.33 0.33 0.33 0.66 0.05
f15 0.33 0.33 0.33 0.66  0.33 0.33 0.33 0.33  0.33 0.33 0.33 0.66 0.05
f16 0.33 0.33 0.33 0.66  0.33 0.33 0.33 0.33  0.33 0.33 0.33  0    0.05
f17 0.33 0.33 0.33 0.33  0.33 0.33 0.33   0    0.33 0.33 0.33 0.66 0.05
f18 0.33 0.33 0.33 0.33  0.33 0.33 0.33 0.66  0.33 0.33 0.33  0    0.05
f19 0.33 0.33 0.33 0.33  0.33 0.33 0.33 0.66  0.33 0.33 0.33 0.66 0.05
f20 0.33 0.33 0.33 0.66  0.33 0.33 0.33 0.66  0.33 0.33 0.33 0.66 0.05

Uh, yeah. I think that's it. I haven't tested it though. Happy fractaling!

wow thank you!
i'll work on that formulas that you gave me.

From where you get those? from your mind??
may you send me the source please? smiley

and again thank you
« Last Edit: July 05, 2010, 08:14:52 PM by yoniHorn » Logged
Timeroot
Fractal Fertilizer
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Posts: 362


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« Reply #4 on: July 06, 2010, 10:18:08 AM »
Sure thing. Yeah, I got them from my mind. It's just one transform for each of the 20 smaller cubes the make up the Menger sponge; most of the variables are 0.33 because the cube is 1/3 the size; the other three just move the cube to each of the 20 positions.
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Someday, man will understand primary theory; how every aspect of our universe has come about. Then we will describe all of physics, build a complete understanding of genetic engineering, catalog all planets, and find intelligent life. And then we'll just puzzle over fractals for eternity.
yoniHorn
Guest
« Reply #5 on: July 06, 2010, 11:55:56 AM »
Quote from: Timeroot on July 05, 2010, 06:00:10 PM
Ahh, cool! I didn't read your source code, but I'm guessing you've only implemented affine transformations...  From what I know, I guess these follow something like

xNew=a*x+b*y+c*z+d;
yNew=e*x+f*y+g*z+h;
zNew=i*x+j*y+k*z+l;

Maybe something like Sierpinksi pyramid/tetrahedron would be good... I think that would be

w   a   b    c   d    e    f    g   h    i    j    k    l    p
f1 0.5 0.5 0.5  0  0.5 0.5 0.5  0  0.5 0.5 0.5  0 0.25
f2 0.5 0.5 0.5 .5  0.5 0.5 0.5  0  0.5 0.5 0.5  0 0.25
f3 0.5 0.5 0.5  0  0.5 0.5 0.5 .5  0.5 0.5 0.5  0 0.25
f4 0.5 0.5 0.5  0  0.5 0.5 0.5  0  0.5 0.5 0.5 .5 0.25

Note that this won't give you an *equliateral* Sierpinksi pyramid, more a sort of right-angled sierpinksi pyramid. Another simple formula. to make a Menger sponge:

w      a     b      c    d      e      f     g     h       i      j      k    l       p
f1   0.33 0.33 0.33   0    0.33 0.33 0.33   0    0.33 0.33 0.33  0    0.05
f2   0.33 0.33 0.33   0    0.33 0.33 0.33   0    0.33 0.33 0.33 0.33 0.05
f3   0.33 0.33 0.33   0    0.33 0.33 0.33 0.33  0.33 0.33 0.33  0    0.05
f4   0.33 0.33 0.33 0.33  0.33 0.33 0.33   0    0.33 0.33 0.33  0    0.05
f5   0.33 0.33 0.33   0    0.33 0.33 0.33   0    0.33 0.33 0.33 0.66 0.05
f6   0.33 0.33 0.33   0    0.33 0.33 0.33 0.66  0.33 0.33 0.33  0    0.05
f7   0.33 0.33 0.33 0.66  0.33 0.33 0.33   0    0.33 0.33 0.33  0    0.05
f8   0.33 0.33 0.33   0    0.33 0.33 0.33 0.66  0.33 0.33 0.33 0.66 0.05
f9   0.33 0.33 0.33 0.66  0.33 0.33 0.33   0    0.33 0.33 0.33 0.66 0.05
f10 0.33 0.33 0.33 0.66  0.33 0.33 0.33 0.66  0.33 0.33 0.33  0    0.05
f11 0.33 0.33 0.33   0    0.33 0.33 0.33 0.66  0.33 0.33 0.33 0.33 0.05
f12 0.33 0.33 0.33 0.66  0.33 0.33 0.33   0    0.33 0.33 0.33 0.33 0.05
f13 0.33 0.33 0.33 0.66  0.33 0.33 0.33 0.66  0.33 0.33 0.33 0.33 0.05
f14 0.33 0.33 0.33   0    0.33 0.33 0.33 0.33  0.33 0.33 0.33 0.66 0.05
f15 0.33 0.33 0.33 0.66  0.33 0.33 0.33 0.33  0.33 0.33 0.33 0.66 0.05
f16 0.33 0.33 0.33 0.66  0.33 0.33 0.33 0.33  0.33 0.33 0.33  0    0.05
f17 0.33 0.33 0.33 0.33  0.33 0.33 0.33   0    0.33 0.33 0.33 0.66 0.05
f18 0.33 0.33 0.33 0.33  0.33 0.33 0.33 0.66  0.33 0.33 0.33  0    0.05
f19 0.33 0.33 0.33 0.33  0.33 0.33 0.33 0.66  0.33 0.33 0.33 0.66 0.05
f20 0.33 0.33 0.33 0.66  0.33 0.33 0.33 0.66  0.33 0.33 0.33 0.66 0.05

Uh, yeah. I think that's it. I haven't tested it though. Happy fractaling!

sorry but I think that the first formulas are not correct..
when i place the point's in the formula they keep going to infinity instead of staying in the same range..
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lycium
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« Reply #6 on: July 06, 2010, 02:02:25 PM »
hi yoniHorn,

you can simply initialise a random one smiley

the iterated transformation T should be contractive on average; so what you do is choose 3 random basis vectors u, v, w with average magnitude <= 1, then you choose a random offset in some range, maybe +/- 4 even. this can be as big as you like, because the overall contractive factor will pull the points towards the origin.
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yoniHorn
Guest
« Reply #7 on: July 06, 2010, 04:23:10 PM »
Quote from: lycium on July 06, 2010, 02:02:25 PM
hi yoniHorn,

you can simply initialise a random one smiley

the iterated transformation T should be contractive on average; so what you do is choose 3 random basis vectors u, v, w with average magnitude <= 1, then you choose a random offset in some range, maybe +/- 4 even. this can be as big as you like, because the overall contractive factor will pull the points towards the origin.
alright I think I understand it now..
can you please show me how you build this king of transformation?
i got the idea but not how to apply it..


BTW the Sierpinksi pyramid is working Great!!
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cKleinhuis
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Posts: 7044


formerly known as 'Trifox'


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« Reply #8 on: July 06, 2010, 04:43:22 PM »
you form (4d) vectors to fill variables a,b,c,d e,f g,h i, j,k,l


xNew=a*x+b*y+c*z+d;
yNew=e*x+f*y+g*z+h;
zNew=i*x+j*y+k*z+l;

just make sure the magnitudes of the vectors are smaller than 1 to achieve a contractive transformation...
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