Simple Sierpinsky

[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:

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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  }
}

[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.

[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 }
}

[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 }
}

[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

[romulusnr]

One wishes it could be done without explicit trigonometry...

[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.

[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.....