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December 24, 2007
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:iconmakinmagic:
Created using Ultrafractal.

Another inspired by Dirk Monteny's work.
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:icondark-beam:
=dark-beam Mar 17, 2011  Student Artist
A true wonder! If only I can do this with simple kifs. :)

The M3 formula kifs;

Menger3(x,y,z){
r=x*x+y*y+z*z;
for(i=0;i<MI && r<bailout;i++){
rotate1(x,y,z);

x=abs(x);y=abs(y);z=abs(z);
if(x-y<0){x1=y;y=x;x=x1;}
if(x-z<0){x1=z;z=x;x=x1;}
if(y-z<0){y1=z;z=y;y=y1;}

rotate2(x,y,z);

x=scale*x-CX*(scale-1);
y=scale*y-CY*(scale-1);
z=scale*z;
if(z>0.5*CZ*(scale-1)) z-=CZ*(scale-1);

r=x*x+y*y+z*z;
}
return (sqrt(x*x+y*y+z*z)-2)*scale^(-i);
}

(possible?)

--
My latest releases @ FForums [link]
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:iconmakinmagic:
~MakinMagic Mar 17, 2011  Hobbyist Digital Artist
The Sierpinski Temple itself (exactly as in my full IFS render) can't be (completely) done using KIFS because apart from the (4*3 squares) Menger Carpet style base there are two (possibly 3, I forget) transforms above the "ground" and these are overlapping in terms of their sub-spaces which means that a single linear iteration will not always choose the correct transformation combination and therefore a tree-style iteration is required, though admittedly the tree could be limited to branching in the cases where more than one of the overlapping transforms could apply, rather than is done in my current 3D IFS formula for UF where the full tree is traversed with n branches per iteration where there are n transforms.
Having said that, in this case very careful use of the conditionals in a KIFS formula should be able to get reasonably close I would have thought.

--
The meaning and purpose of life is to give life purpose and meaning.

The instigation of violence is the resort of those lacking spirituality.
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:icondark-beam:
=dark-beam Mar 17, 2011  Student Artist
Omg, I have enouhh troubles with the normal transforms! i better stay away :)

--
My latest releases @ FForums [link]
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:iconlordkorv:
and who is worshiped here?
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:iconmakinmagic:
~MakinMagic Feb 3, 2011  Hobbyist Digital Artist
Well, Sierpinski I guess ;)
Just Google him !

--
The meaning and purpose of life is to give life purpose and meaning.

The instigation of violence is the resort of those lacking spirituality.
Reply
:icondspwhite:
As you might guess, I've tried to experiment with variations of the Menger sponge, but I can't get anything as good as this yet.

Great work.
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:iconmakinmagic:
Mood: Joy ~MakinMagic Nov 20, 2009  Hobbyist Digital Artist
Thanks.
Part of the trick to these is create some sort of 2D carpet at ground level then add two or more transforms above some of which are inverted.

--
The meaning and purpose of life is to give life purpose and meaning.

The instigation of violence is the resort of those lacking spirituality.
Reply
:iconrhunel:
That's INSANE!

--
"A bruised reed He will not crush." --
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:iconmakinmagic:
Mood: Joy ~MakinMagic Jul 10, 2008  Hobbyist Digital Artist
Thanks, I think :)

--
The meaning and purpose of life is to give life purpose and meaning.

The instigation of violence is the resort of those lacking spirituality.
Reply
:iconrhunel:
It means it's astoundingly good. I couldn't imagine something like that could be created, and you did!

--
"A bruised reed He will not crush." --
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