4D  structures, a short algorithm.

The algorihm uses vectors, which are combined by the dot product (scalar multiplication). Since the scalar product is defined in any dimension, the program also generates structures in 4D - space. The results are attractors of a sort of self-organization.

The Java-program Graph4D.jar creates 4D-structures, which are projected to a 2D picture.



Graph4D Panel

New Run - Button: Starts a run with new initial conditions. The Parameters e and s are unchanged.

Clear - Button  : Only the screen is cleared.

Cross section - Check Box: Current slice plane.
Strobe - Check Box       : Continuous application of the Clear - Button.

+  e-parameter -   : Change of e-parameter. Step width is 1.
+  s-parameter -   : Change of s-parameter. Step width is 1.
+      x       -   : Shift of the image in x-direction.
+      y       -   : Shift of the image in y-direction.
+     Zoom     -   : Change of Magnification. Factor is 2 and 1/2.

Examples - Button  : Switch for different graphs with up to 6 knots and 15 edges.
Projection - Button: Projection of the 4D - structure into 6 different 2D planes.

Left textfield     : Current e-parameter.
Right textfield    : Current s-parameter.