2
$\begingroup$

I plot two square lattices where one of them is rotated by 30 degrees. The Mathematica command to generate them is

{GridGraph[{5, 5}], Rotate[GridGraph[{5, 5}], 30]}

but I wonder whether it is possible to plot them right on top of each other to generate a Moire grid?

see here for instance

Improve this question
$\endgroup$
2
  • $\begingroup$ @Syed you are a mathematica magician :) thanks $\endgroup$
    – Joseph
    Commented Aug 13, 2021 at 15:03
  • $\begingroup$ Overlay[{GridGraph[{5, 5}], Rotate[GridGraph[{5, 5}], 45 Degree]}, Alignment -> Center] I forgot to write Degree, so deleted the previous comment. $\endgroup$
    – Syed
    Commented Aug 13, 2021 at 17:54

1 Answer 1

Reset to default
2
$\begingroup$ 
g1 = GridGraph[{5, 5}]

enter image description here

We can use RotationTransform and GraphEmbedding to rotate the vertex coordinates of the input graph:

ClearAll[rotateVCoords]

rotateVCoords[angle_: 30 Degree] := RotationTransform[angle, Mean @ #] @ 
  # &[GraphEmbedding @ #] &

SetProperty[g1, VertexCoordinates -> rotateVCoords[][g1]]

enter image description here

frames = Show[g1, 
    SetProperty[g1, VertexCoordinates -> rotateVCoords[# Degree][g1]],
     PlotRange -> MinMax /@ Transpose[rotateVCoords[45 Degree][g1]], 
    PlotRangePadding -> Scaled[.05]] & /@ Range[0, 360, 3]; 

Export["rotatevcoords.gif", frames, AnimationRepetitions -> ∞]

enter image description here

We can use rotateVCoords in two ways: (1) With Show + SetProperty to get a Graphics object, (2) With GraphUnion + IndexGraph to get a Graph object as output:

ClearAll[rotateAndCombineToGraphics, rotateAndCombineToGraph]

rotateAndCombineToGraphics[angle_: 30 Degree] := 
 Show[#, SetProperty[#, VertexCoordinates -> rotateVCoords[angle][#]]] &

rotateAndCombineToGraph[angle_: 30 Degree] := 
 GraphUnion[#, IndexGraph[#, 1 + VertexCount @ #], 
   VertexCoordinates -> Join[GraphEmbedding @ #, rotateVCoords[angle][#]], ##2] &

Examples:

rotateAndCombineToGraphics[] @ g1

enter image description here

Head @ %

Graphics

rotateAndCombineToGraph[] @ g1

enter image description here

Head @ %

Graph

With the second approach, we can add Graph options:

rotateAndCombineToGraph[][g1, 
 ImageSize -> Large, 
 VertexSize -> Scaled[.03], 
 VertexLabels -> {v_ :> Placed[Mod[v, VertexCount[g1], 1], Center]}]

enter image description here

rotateAndCombineToGraph[45 Degree][g1, 
 ImageSize -> Large, 
 VertexSize -> Scaled[.03], 
 VertexLabels -> {v_ :> Placed[Mod[v, VertexCount[g1], 1], Center]}, 
 VertexStyle -> {v_ :> If[v > VertexCount[g1], Yellow, LightBlue]}, 
 EdgeStyle -> {_ :> Red, Alternatives @@ EdgeList[g1] :> Gray}]

enter image description here

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.