Wolfram: Mesh Region Examples

SierpinskiMesh

• SierpinskiMesh

Table[ SierpinskiMesh[x] , {x, 1, 4}]

Table[ SierpinskiMesh[x,3] , {x, 1, 4}]

MengerMesh

• MengerMesh

Table[ MengerMesh[x] , {x, 1, 3}]

Table[ MengerMesh[x,3] , {x, 1, 3}]

CantorMesh

• CantorMesh

Table[ CantorMesh[x,1] , {x, 1, 3}]

Table[ CantorMesh[x,2] , {x, 1, 3}]

Table[ CantorMesh[x,3] , {x, 1, 3}]

DelaunayMesh

• DelaunayMesh

DelaunayMesh[RandomReal[{-10, 10}, {50, 2}], Axes -> True]

xdelu = DelaunayMesh[RandomReal[{-10, 10}, {50, 3}], Axes -> True,
   Boxed -> True];

HighlightMesh[xdelu,
{Style[0, Directive[PointSize[Large], Red]],
 Style[1, Blue],
 Style[2, Opacity[0.5]]}]

VoronoiMesh

• VoronoiMesh

xpoints = RandomReal[{-1, 1}, {25, 2}];
xvmesh = VoronoiMesh[ xpoints];
Show[{xvmesh, Graphics[{Red, Point[xpoints]}] }]

(* 3d example of VoronoiMesh *)
(* xtodo *)

xpoints = RandomReal[{-1, 1}, {25, 3}];
xvmesh = VoronoiMesh[ xpoints];
Show[{xvmesh, Graphics3D[{Style[Point[xpoints], Red, Opacity[0.5]]}] }]

xpoints = RandomReal[{-1, 1}, {25, 3}];
VoronoiMesh[ xpoints, MeshCellStyle -> {{0, All} -> Red, {2, All} -> Opacity[0.5]}]