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Sierpinski Temple
By MakinMagic
19 Favourites25 Comments4K Views
Created using Ultrafractal.
Another inspired by Dirk Monteny's work.
Another inspired by Dirk Monteny's work.
Image details
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768x768px 197.53 KB
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© 2007 - 2021 MakinMagic
Comments25
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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?)
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?)
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.
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.
Omg, I have enouhh troubles with the normal transforms! i better stay away
and who is worshiped here?
Well, Sierpinski I guess 
Just Google him !
Just Google him !
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.
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.
That's INSANE!
Thanks, I think
It means it's astoundingly good. I couldn't imagine something like that could be created, and you did!
Thanks very much.
Thanks
Fantastic!
Thanks very much.
nice!
very complex looking!
very complex looking!
Thank you.
Welcome!
great work dave! 
Thanks Thomas !
Incredible!Thanks !
a tip dirk gave me...skew the z plane to 180 ..creates some interesting variations
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