Distorsion of the Menger Sponge -iteration 2- [Distorsion de l'éponge de Menger -itération 2-].
A tridimensional object is defined as a set of points P={X,Y,Z}.
To each point P is associated the following octonion O={X,Y,Z,0,0,0,0,0}.
Then each octonion O is submitted to the transformation:
e2
A.O + B
O --> O' = -----------
e1
C.O + D
with {e1,e2} being two arbitrary real numbers and {A,B,C,D} four arbitrary octonions.
At last a new point P' is defined with {X',Y',Z'} being arbitrary linear combinations of the components of O'. The set of points P' defines a new tridimensional object...
Nota: the radius and the colors of each particle visualizing a point P' vary according to its {X',Y',Z'} coordinates...
See some related pictures:
(CMAP28 WWW site: this page was created on 05/31/2022 and last updated on 07/07/2024 12:18:11 -CEST-)