Скачать или смотреть SmoothLife in Matlab with an increasing time differential

This is an implementation of SmoothLife with Matlab. The time differential is varied over time, resulting in evolving behavior. Shown in the main window is the current data; the calculated state and neighborhood corresponding to the displayed data are shown to the right on the top and bottom (respectively).

SmoothLife is a continuous extension of Conway's Game of Life published in Stephan Rafler's 2011 paper "Generalization of Conway’s ”Game of Life” to a continuous domain - SmoothLife."

Like the Game of Life, the state of a cell transitions based on the neighbors and a transition function. In SmoothLife, the 'state' and 'neighborhood' of a cell is determined by the circular and annular area integral at each infinitesimal point. The transition function is a smooth function of the state and neighborhood (essentially using a few sigmoid functions); birth/survival intervals are analogous to the Game of Life.

Rafler suggests multiple variants of making the timestep continuous such that an infinitesimal time can be calculated. I have been unsuccessful with the techniques suggested in the paper, but found interesting results by calculating: new_state = current_state + (transition - current_state) * dt.

The results of increasing dt over time (without resetting the simulation) are shown. In Matlab notation, each timestep dt was increased to the next value in the vector [0.75:0.0002:0.83 0.92:0.0001:1.15]. It's a fairly interesting result because the characteristics change very significantly over this range.