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.