Hilbert's 13th Problem

SetDirectory["C:\\drorbn\\AcademicPensieve\\2014-11\\H13"]

Pensieve Header: Hilbert's 13th problem - Step 2 (2014 Branch).

<< "../../2009-11/Hilbert13th-Program.m"

ϕ1:= Phi[Identity, 2, 0.3, 2/3];
ϕ2:= Phi[ϕ1, 12, 0, 0.95];

phi1:= Phi[Identity, 2, 0.3, 2/3];
phi2:= Phi[phi1, 12, 0, 0.8];
phi3:= Phi[ϕ, ϕ0 -> phi1, Subdivisions -> 12, Slope -> 0, FillFactor -> 0.8];
g1=G[f, phi1];
g2=G[f, phi2];

Step2Cascade=Rasterize[
Plot3D[ϕ2[x]+λ*ϕ2[y], {x,0,1}, {y,0,1},
PlotPoints -> 479, Mesh -> 23,ViewPoint -> {-2,-2,1}, NormalsFunction -> None, Boxed -> False, Axes -> None, ColorFunction -> Automatic, ColorFunctionScaling->True
]
];

Export[
"Step2Cascade.png",
ImageCrop[Step2Cascade]
]

res=4000;
Timing[
Step2CascadeWithG2=Rasterize[
Plot3D[phi2[x]+λ*phi2[y], {x,0,1}, {y,0,1},
PlotPoints -> 3res/4-1, Mesh -> 11,ViewPoint -> {-2,-2,1}, NormalsFunction -> None, ColorFunction -> (Hue[g2[#3]]&), ImageSize -> res, Axes ->None, Boxed -> False
], ImageSize -> res, RasterSize -> res
];
]

Export[
"Step2CascadeWithG2.png",
Step2CascadeWithG2, ImageSize -> res, RasterSize -> res
]