A series of phase spaces

A phase space is the set of all possible solutions to a problem. 3D renderings of phase spaces from 3 to 14 variables are displayed. After 14 variables, my computer ran out of memory. In the case of the 14D phase space, 16,384 possible solutions exist. In the case of the 3D phase space, 8 possible solutions exist. Each solution is illustrated with a blue dot and the distance between the dots represents the similarity of the solutions. The R source code used to generate it is included below.

An amazing hidden world of high dimensional phase spaces is revealed to get lost in and let your mind wander.

14D phase space

13D phase space

12D phase space

11D phase space

10D phase space

9D phase space

8D phase space

7D phase space

6D phase space

5D phase space

4D phase space

3D phase space

R source code used - a bit rough and ready.