Random image generation

RandomReal[{0,1},{360,360,3}]//Image

Probability of getting the cat

((.1)^(360 360))
"10^-"ToString[360 360]

Full image space and the target manifold

res=360;

(* manifold edges: *)
blueSeq=
{,,,,,,,,,,,,,,,,,,,};
yellowSeq=
{,,,,,,,,,,,,,,,,,,,};
blueSeq=ImageResize[#,res]&/@blueSeq;
yellowSeq=ImageResize[#,res]&/@yellowSeq;

(* noise corners *)
NoiseBlend[{img1_,img2_},α_]:=ImageAdd[(img1-.5)Cos[.5 π α],(img2-.5)Sin[.5 π α],.5];
Noise[res_]:=Image[RandomReal[NormalDistribution[0.5,0.2],{res,res,3}]];

noises=Blend[{Noise[res],ImageResize[Noise[res/2],res]},.25]&/@Range[4];

"images"

ManifoldPlot[X_,Y_,α_]:=Module[{f,P3,Pf},
f[x_,y_]:=-.1x+.14y-.3Sin[x y]+0.05(y^3)-.07Cos[(x^2)+(y^2)]-.2;
P3={X,Y,f[X,Y](1-Abs[α])+α};
Pf={X,Y,f[X,Y]};
Show[{
Plot3D[f[x,y],{x,-1.05,1.05},{y,-1.05,1.05},PlotRange->1.05{{-1,1},{-1,1},{-1,1}},BoxRatios->{1,1,1},SphericalRegion->True,Mesh->None,Boxed->False,BoundaryStyle->None,Axes->False,PlotStyle->Directive[Opacity[.5,RGBColor["#4159e1"]],Specularity[.2],EdgeForm[]],Lighting->"Neutral"]
,
Graphics3D[{Opacity[.1,Gray],Cuboid[1.05{-1,-1,-1},1.05{1,1,1}],
Opacity[.5,Purple],Sphere[P3,.05],
Dashing[.02],Thickness[0.01],Line[{Pf,P3}]
}]
}]
];

ManifoldImage[X_,Y_,α_]:=Module[{f,x,y,duration=blueSeq//Length,manifold,noise},
x=(X+1)/2;
f=Max[Ceiling[duration*x],1];
y=(Y+1)/2;
manifold=Blend[{yellowSeq[[f]],blueSeq[[f]]},y];
noise=NoiseBlend[{NoiseBlend[noises[[;;2]],x],NoiseBlend[noises[[3;;]],x]},y];
NoiseBlend[{NoiseBlend[{manifold,noise},Abs[α]],noise},Abs[α]]
];
"plots"

Manipulate[
Row[{
Show[ManifoldPlot[x,y,α],ImageSize->res],
Show[ManifoldImage[x,y,α],ImageSize->res]
}]
,{{x,0},-1,1},{{y,0},-1,1},{{α,0},0,1}]