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MathMod — Menger Level 4
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Published: 2015-10-26 12:06:51 +0000 UTC; Views: 239; Favourites: 1; Downloads: 1
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Description
The Menger Sponge is a three-dimensional generalization of the Cantor set and Sierpinski carpet. It was first described by Karl Menger in 1926.{
"Iso3D": {
"Description ": ["Menger Sponge Level 4 by Abderrahman Taha 23/10/2015"],
"Name": ["Menger Sponge Level 4"],
"Component": ["MengerSponge"],
"Fxyz": [" - (Dx + Dy + Dz -1)*(((abs(x) >1/3 | abs(y) > 1/3)*(abs(z) >1/3 | abs(y) > 1/3)*(abs(x) >1/3 | abs(z) > 1/3))*( (Cx*(Cy+Cz) + Cz*Cy) =0)*( (Bx*(By+Bz) + Bz*By) =0)*( (Ax*(Ay+Az) + Az*Ay) =0) ) "],
"Varu": [" A = ((abs(u-2/3) <1/81)+ (abs(u-20/27) <1/81)+ (abs(u-16/27) <1/81)+(abs(u-8/9) <1/81) + (abs(u-26/27) <1/81) + (abs(u-22/27) <1/81) +(abs(u-4/9) <1/81) +(abs(u-14/27) <1/81) +(abs(u-10/27) <1/81) +(abs(u+2/3) <1/81) +(abs(u+16/27) <1/81) +(abs(u+20/27) <1/81) +(abs(u+4/9) <1/81) +(abs(u+10/27) <1/81) +(abs(u+14/27) <1/81) +(abs(u+8/9) <1/81) +(abs(u+22/27) <1/81) +(abs(u+26/27) <1/81) +(abs(u) <1/81) + (abs(u-2/27) <1/81) +(abs(u+2/27) <1/81) +(abs(u-2/9) <1/81) + (abs(u-8/27) <1/81) + (abs(u-4/27) <1/81) +(abs(u+2/9) <1/81)+(abs(u+4/27) <1/81)+(abs(u+8/27) <1/81))",
" B = ((abs(u-2/3) <1/27)+(abs(u-8/9) <1/27) + (abs(u-4/9) <1/27) +(abs(u+2/3) <1/27) +(abs(u+4/9) <1/27) + (abs(u+8/9) <1/27) +(abs(u) <1/27) + (abs(u-2/9) <1/27) + (abs(u+2/9) <1/27))",
"C = ((abs(u-2/3) <1/9) + (abs(u+2/3) <1/9) + (abs(u) <1/9))",
"D = u^100"],
"Xmax": [" 1.001"],
"Xmin": ["-1.001"],
"Ymax": [" 1.001"],
"Ymin": ["-1.001"],
"Zmax": [" 1.001"],
"Zmin": ["-1.001"]
}
}
