Page 1 of 1
Simple Sierpinsky
Posted: Wed Jul 06, 2005 5:15 pm
by romulusnr
This makes a simple right-triangle sierpinsky gasket using the reduction method. RTRI makes a right triangle, we reuse this with an inverted right triangle to pile on the reductions (in truth, we are dropping white triangles on top of black triangles, but the effect is the theoretically the same):
Code: Select all
startshape RTRI2
rule RTRI {
SQUARE {}
RTRI { x -.75 y -.25 s .5 }
RTRI { x .25 y .75 s .5 }
}
rule RTRI2 {
RTRI {}
// actually, this is unnecessary, just use a square and they will accumulate!
// RTRI { r 180 x -1 y 1 b .9 }
SQUARE { x -1 y 1 b .9 }
RTRI2 { x .25 y -.25 s .5 }
RTRI2 { x -.75 y -.25 s .5 }
RTRI2 { x .25 y .75 s .5 }
}
I also have a Menger sponge done the accumulative (i.e. backwards from reductive) way:
Code: Select all
startshape MENGER
rule MENGER {
SQUARE { }
MENGER { y -1 x -1 s .3333 }
MENGER { y -1 x 0 s .3333 }
MENGER { y -1 x 1 s .3333 }
MENGER { y 0 x -1 s .3333 }
// you don't want one in the middle!
//MENGER { y 0 x 0 s .3333 }
MENGER { y 0 x 1 s .3333 }
MENGER { y 1 x -1 s .3333 }
MENGER { y 1 x 0 s .3333 }
MENGER { y 1 x 1 s .3333 }
}
Posted: Wed Jul 06, 2005 5:51 pm
by aaronstj
Well done. I'll have to try this method for making a "classic" Serpinski's triangle. The trig is starting to hurt my brain, though.
Posted: Wed Jul 06, 2005 8:45 pm
by doofsmack
"classic" Sierpinsky triangle using this method:
Code: Select all
startshape sierpinsky
rule sierpinsky {
triangle {}
triangle { s .5 b 1 r 180 }
sierpinsky { s .5 x -.25 y -.144337 }
sierpinsky { s .5 x .25 y -.144337 }
sierpinsky { s .5 y .288675 }
}
rule triangle {
left { y .144337 }
right { y .144337 }
}
rule left {
SQUARE { s .25 x -.125 y -.125 }
SQUARE { s .25 x -.125 y -.308012 }
left { s .5 x -.25 y -.216506 }
left { s .5 y .216506 }
}
rule right {
SQUARE { s .25 x .125 y -.125 }
SQUARE { s .25 x .125 y -.308012 }
right { s .5 x .25 y -.216506 }
right { s .5 y .216506 }
}
Posted: Wed Jul 06, 2005 9:11 pm
by aaronstj
Awesome. Saved me a couple of brain cells. For fun, here's your, but using buckyboy314's triangle code, which uses fewer primitives.
Code: Select all
startshape sierpinsky
rule sierpinsky {
triangle {}
triangle { s .5 b 1 r 180 }
sierpinsky { s .5 x -.25 y -.144337 }
sierpinsky { s .5 x .25 y -.144337 }
sierpinsky { s .5 y .288675 }
}
rule triangle {
meta_TRIANGLE{ s .288675}
}
rule meta_TRIANGLE{
TRI{}
TRI{r 120}
TRI{r -120}
}
rule TRI{
SQUARE{x -0.183013 y 0.683013 r -30 }
SQUARE{x 0.183013 y 0.683013 r 30 }
TRI{y 1.1547 s 0.42265 }
}
Posted: Wed Jul 06, 2005 9:25 pm
by doofsmack
That triangle technique is pretty clever. I can't believe I missed it. It would have saved me more than a couple brain cells
Posted: Fri Jul 08, 2005 12:19 pm
by romulusnr
One wishes it could be done without explicit trigonometry...
Posted: Fri Jul 08, 2005 2:27 pm
by MtnViewJohn
The next version will have a TRIANGLE primitive and you will be able to control the order of transforms. Being able to do a rotate before a translate will eliminate a lot of explicit trig.
Posted: Fri Jul 08, 2005 2:35 pm
by aaronstj
Controlling the order of transforms would be nice.
Another thing that would help with the geometry problem would be if you allowed mathmatical expressions instead of just numeric constants. I'm not saying that you should allow variables or anything that breaks the context free principle, but it would be nice to be able to say, for example "sqrt(3) / 3" rather than "0.577350" and having to remember what the hell that number is for later. Using expressions would also make it easier for other people to see how your designs work, and it would help with round off artifacts (since the precision of a double is certainly more than the precision of however many digits I'm willing to copy from calc).
Named constants would also be nice, but I digress.....