Wolfram Cloud Document

Additional examples for the first discussion and second discussion

Give DALL.E a piece of WL code that produces a graphics and that is not straightforward to predict in detail. It is interesting (and entertaining) to see how it ‘understands’ the code and predicts what the result could look like.

DALL·E 2 prompt

Analyze the following code carefully and make an artistic rendering of how you think the result would look like:

The Wolfram Language input code and its output graphics

ContourPlot3D[(*implicitformofthedoubletorus*)((x-1/3)^2+y^2-1/144)*((x+1/3)^2+y^2-1/144)*(x^2+4y^2+25z^2-1)==-1/200,{x,-1.01,1.01},{y,-0.51,0.51},{z,-0.21,0.21},BoxRatios->Automatic,ContourStyle->Brown]

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DALL-E AI prediction from reading the input code

The Wolfram Language input code and its output graphics

torus[{x_,y_,z_},R_,r_]:=(x^2+y^2+z^2)^2-2(R^2+r^2)(x^2+y^2)+2(R^2-r^2)z^2+(R^2-r^2)^2;ContourPlot3D[Evaluate[(*sixtori*)torus[{x,y,z}-{+1.6,+1.6,0},1,0.4]*torus[{x,y,z}-{+1.6,-1.6,0},1,0.4]*torus[{x,y,z}-{-1.6,+1.6,0},1,0.4]*torus[{x,y,z}-{-1.6,-1.6,0},1,0.4]*torus[{y,z,x}-{0,+1.6,0},1,0.4]*torus[{y,z,x}-{0,-1.6,0},1,0.4](*makenonfactorizable*)==10^7],{x,-3,3},{y,-3,3},{z,-3,3}]

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DALL-E AI prediction from reading the input code

The Wolfram Language input code and its output graphics

In[]:=

torus[φ1_,φ2_,r1_,r2_]={r1Cos[φ1]+r2Cos[φ1]Cos[φ2],r1Sin[φ1]+r2Sin[φ1]Cos[φ2],r2Sin[φ2]};Manipulate[With[{den=Denominator[h]},ParametricPlot3D[torus[φ1,hφ1,R,1]+storus[φ1+δ,h(φ1+δ),R,1],{φ1,0,den2Pi},{s,0,1},Mesh->False,MaxRecursion->0,PlotPoints->{60den,12},Boxed->False,Axes->False]],{{δ,2.72,"shift"},-2Pi,2Pi},{{h,21/5,"torus knot index"},1/5,5,1/5},{{R,1.5,"torus radius"},0,6},TrackedSymbols:>True,SaveDefinitions->True]

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