Please first check the examples tab (.mlx doc) here on the right for a complete description.
Once downloaded, typewrite 'doc Sierpinski_ball' or 'help Sierpinski_ball' in Matlab console for support.
To benefit from the file documentation attached, be sure to download the file, not to just copy and paste it.
N.B. : level 0 corresponds to the volumic mesh of the unit ball (radius = 1).
Mathworlds (2021). Sierpinski ball (https://github.com/NicolasDouillet/sierpinski_ball/releases/tag/v4.0), GitHub. Retrieved .
Color rendering used for this cover image is radius based, i.e. by computing each vertex distance to the origin : C = sqrt(sum(V.^2,2)); trisurf(T,V(:,1),V(:,2),V(:,3),C); colormap('jet');
Default maximum number of iterations and sampling steps (nb_max_it) set to 7. Increase it line 84.
A function to compute a Sierpinski ball. Giving the resulting sets of vertices and triangles, it is almost 3D printing ready. Just have to write them in a .ply file for instance. The fractal object thereby created is a fractal sponge.
The algorithm principle is based on the projection of the Sierpinski triangular faces of a regular octahedron on the surface of the unitary sphere.
It is available for 3D printing in my Sculpteo online shop at iteration #3 :
NB : function sample_triangle isincluded, but may also be found independently here :
You may also have a look at some additional views here :
Tip : from nb_iterations = 3, and if using write_ply.m you struggle with displaying the set out of Matlab [...] try to replace in the file header "uchar ushort" by "uint8 uint32" this may help ;-)
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