4 ms·

I'm curious why the particles don't return their their exact original location.

• lutusp 13y ago
  That's a common behavior in Canvas programs where particles are plotted on integer boundaries. The plotting routines have to decide which pixel gets the paint, and the argument is a float with an ambiguous mantissa. Round off to an integer, and you get the next higher or lower location. If the routine were written to add 0.5 to each coordinate, that effect would go away and the particles would (apparently) return to their original locations. In this case, the model is one of exponential decay, meaning over time the particles move toward a target coordinate at a speed determined by the remaining distance, with this ODE: f(t) = y(t) - y'(t) * tc == c Where: y = a value that changes with respect to time t = time c = final position (the value toward which y(t) moves) tc = decay time constant f(t) = an unknown function that meets the description provided by the listed terms, but in this case equal to: f(t) = (1-e^-(t/tc)) * c More or less. The result of the uncertain outcomes for the particles is that many outcomes drift toward, but don't quite get to, their originally assigned integer coordinates. Then for plotting they're rounded up or down based on small numerical errors, producing the display you see. Again, this problem can be solved by adding 0.5 to all plotting coordinates before rounding.
  • hadem 13y ago
    Thanks for the explanation!