Self-Similarity and Fractals 2018 design challenge:
1) design a fractal chair
2) build and test the fractal chair for strength and durability

A 3d printed chair ( small enough to be cheap) would be a valid entry.

We need :
1) contestants
2) judges
3) entry forms
4) a winner’s prize

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

Re: Self-Similarity and Fractals 2018 design challenge:

(* Mathematica*)
(* the martian symmetrical chair*)
(* a Sierpinski basket chair*)
(* triangle function*)
Clear[f, g, t]
f[t_] = Cos[t]/Max[Cos[t], -Sin[π/6 - t], -Sin[π/6 + t]];
g[t_] = Sin[t]/Max[Cos[t], -Sin[π/6 - t], -Sin[π/6 + t]];
g1 = ParametricPlot[{{f[t], g[t]}, {-f[t] + 2, g[t]}, {-f[t] - 1,
g[t] + Sqrt[3]}, {-f[t] - 1, g[t] - Sqrt[3]}, {-f[t]/2 + 3,
g[t]/2}, {-f[t]/2 - 3/2, g[t]/2 + Sqrt[3] + 3/4 + 1/12}, {-f[t]/2 - 3/2,
g[t]/2 - Sqrt[3] - 3/4 - 1/12}, {f[t]/2 + 2, g[t]/2}, {f[t]/2 - 1,
g[t]/2 + Sqrt[3]}, {f[t]/2 - 1, g[t]/2 - Sqrt[3]}}, {t, -Pi, Pi}]

w = {{f[t], g[t]}, {-f[t] + 2, g[t]}, {-f[t] - 1, g[t] + Sqrt[3]}, {-f[t] - 1, g[t] - Sqrt[3]}, {-f[t]/2 + 3, g[t]/2}, {-f[t]/2 - 3/2,
g[t]/2 + Sqrt[3] + 3/4 + 1/12}, {-f[t]/2 - 3/2,
g[t]/2 - Sqrt[3] - 3/4 - 1/12}, {f[t]/2 + 2, g[t]/2}, {f[t]/2 - 1,
g[t]/2 + Sqrt[3]}, {f[t]/2 - 1, g[t]/2 - Sqrt[3]}};
www = Table[{w[[i, 1]]/9, -w[[i, 2]]/9, (-1 - 0.75)/2}, {i, Length[w]}];
g1 = ParametricPlot3D[
Join[www,
Table[{2*w[[i, 1]], 2*w[[i, 2]],
1 - w[[i]].w[[i]]}/(1 + w[[i]].w[[i]]), {i, Length[w]}]], {t, -Pi,
Pi}, PlotStyle -> Brown, Axes -> False, ImageSize -> 1000,
PlotRange -> All, Boxed -> False] /.
Line[pts_, rest___] :> Tube[pts, 0.05, rest];
Show[g1, ViewPoint -> Top];
Show[g1, ViewPoint -> Front];
(* Euler rotation matrices*)
s[0] = {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}};
s[1] = {{Cos[t], Sin[t], 0},
{-Sin[t], Cos[t], 0},
{0, 0, 1}} /. t -> N[2*Pi/6];
s[2] = {{Cos[t], 0, Sin[t]},
{0, 1, 0},
{-Sin[t], 0, Cos[t]}};

s[3] = {{1, 0, 0}, {0, Cos[t], Sin[t]},
{0, -Sin[t], Cos[t]}} /. t -> N[2*Pi/3];
s[4] = {{Cos[t], Sin[t], 0},
{-Sin[t], Cos[t], 0},
{0, 0, 1}} /. t -> N[-2*Pi/6];
www2 = Table[{w[[i, 2]]/9, 0, w[[i, 1]]/9} + {1/2,
0, (-1 - 0.75)/2 - 0.5}, {i, Length[w]}];
www3 = Table[
s[1].{w[[i, 2]]/9, 0, w[[i, 1]]/9} + {-1/4,
N[Sqrt[3]/4], (-1 - 0.75)/2 - 0.5}, {i, Length[w]}];
www4 = Table[
s[4].{w[[i, 2]]/9, 0, w[[i, 1]]/9} + {-1/4, -N[Sqrt[3]/4], (-1 - 0.75)/2 - 0.5}, {i, Length[w]}];
g0 = ParametricPlot3D[{www2, www3, www4}, {t, -Pi, Pi}, PlotStyle -> Brown, Axes -> False, ImageSize -> 1000, PlotRange -> All, Boxed -> False] /. Line[pts_, rest___] :> Tube[pts, 0.05, rest];
gw = Show[{g0, g1}, ViewPoint -> {5, 5, 5}, Background -> Pink]
(end)
My example:

https://i.pinimg.com/564x/9b/b3/5f/9bb35fe6cbc4ad1a67bffa485edc9cd8.jpg

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

A second example:
(* mathematica*)

pieces = {{0, 0, 0}, {0, 0, 1}, {0, 0, 2}, {0, 0, 3}, {0, 0, 4}, {0,
1, 0}, {0, 1, 1}, {0, 1, 3}, {0, 1, 4}, {0, 2, 0}, {0, 2, 4}, {0,
3, 0}, {0, 3, 1}, {0, 3, 3}, {0, 3, 4}, {0, 4, 0}, {0, 4, 1}, {0,
4, 2}, {0, 4, 3}, {0, 4, 4}, {1, 0, 0}, {1, 0, 1}, {1, 0, 3}, {1,
0, 4}, {1, 1, 0}, {1, 1, 1}, {1, 1, 3}, {1, 1, 4}, {1, 3, 0}, {1,
3, 1}, {1, 3, 3}, {1, 3, 4}, {1, 4, 0}, {1, 4, 1}, {1, 4, 3}, {1,
4, 4}, {2, 0, 0}, {2, 0, 4}, {2, 4, 0}, {2, 4, 4}, {3, 0, 0}, {3,
0, 1}, {3, 0, 3}, {3, 0, 4}, {3, 1, 0}, {3, 1, 1}, {3, 1, 3}, {3,
1, 4}, {3, 3, 0}, {3, 3, 1}, {3, 3, 3}, {3, 3, 4}, {3, 4, 0}, {3,
4, 1}, {3, 4, 3}, {3, 4, 4}, {4, 0, 0}, {4, 0, 1}, {4, 0, 2}, {4,
0, 3}, {4, 0, 4}, {4, 1, 0}, {4, 1, 1}, {4, 1, 3}, {4, 1, 4}, {4,
2, 0}, {4, 2, 4}, {4, 3, 0}, {4, 3, 1}, {4, 3, 3}, {4, 3, 4}, {4,
4, 0}, {4, 4, 1}, {4, 4, 2}, {4, 4, 3}, {4, 4, 4}};


Length[pieces];
N[Log[Length[pieces]]/Log[5]];

menger[cornerPt_, sideLen_, n_] :=

menger[cornerPt + #1*(sideLen/5), sideLen/5, n - 1] & /@ pieces;
menger[cornerPt_, sideLen_,
0] :=
{ColorData["DarkBands"][
N[(0.0625*1.5)*Apply[Plus, cornerPt]]], EdgeForm[],
Cuboid[cornerPt, cornerPt + sideLen*N[{1, 1, 1}]]};
Clear[f]
f[n_] := Flatten[
Join[menger[{6 - n, 0, n}, 1, n], menger[{n, 0, n}, 1, n]]]
g = Show[Graphics3D[
Table[Flatten[menger[{2 - n, 0, -n}, 1, n]], {n, 2}],
Boxed -> False, ImageSize -> 1000, Background -> LightPurple,
ViewPoint -> {-5, -5, 5}],
Graphics3D[Flatten[menger[{1, 0, -2}, 1, 3]]]];
Export["CrossChair2.jpg", g]
(* end*)
https://www.pinterest.com/pin/293648838197696511/

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)