Dror Bar-Natan: Talks: Fields-0911:

Dror Bar-Natan: Academic Pensieve: 2009-11:

Hilbert's 13th Problem

Pensieve Header: Hilbert's 13th problem - Step 1.

<< C:\drorbn\AcademicPensieve\2009-11\Hilbert13th-Program.m

phi5:= Phi[phi0, 5, 0.1, 0.8];
g=G[f, phi5];

Step1G=Rasterize[
Plot[
g[z], {z,0,1+λ},
PlotStyle -> Thick, AxesStyle -> Thick
]
]

Export[
"C:/drorbn/AcademicPensieve/2009-11/Step1G.png",
ImageCrop[Step1G]
]

Timing[
Step1Cascade=Rasterize[
Plot3D[phi5[x]+λ*phi5[y], {x,0,1}, {y,0,1},
PlotPoints -> 51, Mesh -> 14, Exclusions -> None, ViewPoint -> {-2,-2,1}, AxesLabel ->Automatic, NormalsFunction -> None
]
]
]

Export[
"C:/drorbn/AcademicPensieve/2009-11/Step1Cascade.png",
ImageCrop[Step1Cascade]
]

Timing[
Step1CascadeWithG=Rasterize[
Plot3D[phi5[x]+λ*phi5[y], {x,0,1}, {y,0,1},
PlotPoints -> 301, Mesh -> 14, Exclusions -> None, ViewPoint -> {-2,-2,1}, AxesLabel ->Automatic, NormalsFunction -> None, ColorFunction -> (Hue[g[#3]]&)
]
]
]

Export[
"C:/drorbn/AcademicPensieve/2009-11/Step1CascadeWithG.png",
ImageCrop[Step1CascadeWithG]
]

Timing[
Step1Density=Rasterize[
DensityPlot[
g[phi5[x]+λ*phi5[y]], {x,0,1}, {y,0,1}
]
]
]

Export[
"C:/drorbn/AcademicPensieve/2009-11/Step1Density.png",
ImageCrop[Step1Density]
]