To extend this concept to surfaces, we merely have to change our definition of distance somewhat. Recall the usual definition of a sphere is that it is the set of all points within some distance of a given point. The basic idea behind all of this is that we want to generalize the concept of a sphere to include curved surfaces. Indeed, a similar idea was proposed in Rafler’s original work to extend SmoothLife to spherical domains but why should we stop there? Geodesic Distance So it seems reasonable that if we could define the neighborhoods in some more generic way, then we could obtain a generalization of the above equations. Looking at the above equations, the only place where geometry comes into the picture is in the computation of the M and N fields. : The size of the effective neighborhood (this is a simulation dependent scale parameter, and should not effect the asymptotic behavior of the system).: Transition smoothness from interval boundary (again, arbitrary but usually about ).: The transition smoothness from live to dead (arbitrary, but Rafler uses ).: The fraction of living neighbors required for a cell to be born (typically ).: The fraction of living neighbors required for a cell to stay alive (typically ). ![]() ![]() ![]() Recall that is the state field and that we have two effective fields which are computed from f:Īnd that the next state of f is computed via the update rule:Īnd we have 6 (or maybe 7, depending on how you count) parameters that determine the behavior of the automata: To understand how this works, let’s first review Rafler’s equations for SmoothLife.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |