WOLFRAM|DEMONSTRATIONS PROJECT

Hysteresis Modeled with Cellular Automata

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white to black transitions
max
increment / step across border
increment / leap up to pure black at border
black to white transitions
0
decrement / step across border
decrement / leap down to pure white at border
black to black transitions
max
increment
no change
white to white transitions
0
decrement
no change
ECA rule 14
rule 14 with hysteresis
ECA rule
14
■
■
■
■
■
■
■
■
new "white" states
new "black" states
steps
12
color scheme
color
new random seed
A k=5, r=1 CA rule with 88 decimal digits
IC
single black pixel
{1763053326766678177665414288525419823697396189653152731580119053228058218955986025313275, 5, 1}
Hysteresis is the lagging of an effect behind its cause. This Demonstration models hysteresis using elementary cellular automata (ECA) by introducing additional color or gray shades that represent additional states as the cells transition between 0 and 1. You can choose the number of additional states by sliding the red and blue triangles in the upper right corner icon. The four toggler bars at the top further define the allowed transitions of the new colors.