Hilbert's 13th Problem

Pensieve Header: Hilbert's 13th problem - Step 2 to level 3.

SetDirectory["C:/drorbn/AcademicPensieve/2014-11/H13/"];
<< "../../2009-11/Hilbert13th-Program.m"

ϕ1:= Phi[Identity, 2, 0.3, 2/3];
ϕ2:= Phi[ϕ1, 8, (0.3^2), 2/3];
ϕ3:= Phi[ϕ2, 32, (0.3^3), 2/3];
Step2phis = Plot[{ x, ϕ1[x], ϕ2[x], ϕ3[x]}, {x,0,1},
PlotPoints -> 1279, ColorFunction -> Automatic, AxesStyle -> Thick, PlotStyle -> {Directive[Red,Thick], Directive[Green,Thick], Directive[Blue,Thick], Directive[Black,Thin]}
]

Timing[
Step3Cascade=Rasterize[
Plot3D[ϕ3[x]+λ*ϕ3[y], {x,0,1}, {y,0,1},
PlotPoints -> 1279, Mesh -> 95,ViewPoint -> {-2,-2,1}, NormalsFunction -> None, Boxed -> False, Axes -> None
]
]
]