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A space-filling curve is one unbroken line through every point of a square, the limit of paths through finer and finer grids.
Each cell repeats an L-system rule: F draws a step, + and โ turn. Level n of the Hilbert curve visits each of the 4โฟ cells of a 2โฟ ร 2โฟ grid once, its length 2โฟ โ 2โปโฟ nearly doubling each level inside the unit square. The Koch snowflake and the Sierpiลski arrowhead never fill an area: their dimensions are log 4/log 3 โ 1.26 and log 3/log 2 โ 1.58.
Giuseppe Peano found the first in 1890, and David Hilbert drew a simpler one in 1891.
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ใใชใไน
ใ
ใซใพใจใใซๆใใ้ฃ้ณฅๅใ้ใซๅใใฐใใกใคใซใซใใฆใฆใงใใชใณใชใผใง้ ๅธใใใโฆ๏ผ
Love is a ridiculously infinite omnipotent force that always exponentially manifests, ripples and emanates itself forever.
I love seing it happen all over again.
I wonder if it has seen me.
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#ใคใถใใGLSL for(float i,g,e,s;++i<79.;){vec3 p=vec3((FC.xy-.5*r)/r.y*2.+vec2(0,1),g-.5);p.zx*=rotate2D(t*.5);s=1.;for(int i;i++<16;p=vec3(2,5,3)-abs(abs(p)*e-vec3(3,1.4,4.5)))s*=e=max(1.005,8./dot(p,p));g+=mod(length(p.xz),p.y)/s;s=log(s)/g;o.rgb+=hsv(.4*p.y,1.-p.y,s/2e4);}























