Fractal Iterative Dynamics (FracDyn)
Math

These are the functions on the Scenarios menu.

Logistic Map xi+1 = s xi (1 - xi) 0 <= s <= 4
Tent Map
for x <= ½ : xi+1 = s xi
for x > ½ : xi+1 = s (1 - xi)
0 <= s <= 2
Sine Map xi+1 = s sin(pi xi) 0 <= s <= 1
Cubic Map 1 xi+1 = s (xi2)(1 - xi) 0 <= s <= 6.75
Cubic Map 2 xi+1 = s xi(1 - xi)2 0 <= s <= 6.75
Quartic Map xi+1 = s (xi2) (1 - xi)2 0 <= s <= 16
Discontinuous Map Let d = x value of discontinuity (set via Parameters button)

if (d < 0.5) :
for (0 <= xi <= d) : xi+1 = ( s / ( 2 d (1 - d) ) ) xi (1 - xi)
for (d < xi <= 0.5) : xi+1 = s xi
for (0.5 < xi <= 1) : xi+1 = s - s xi

else if (d >= 0.5) :
for (0 <= xi <= d) : xi+1 = s xi (1 - xi)
for (d < xi <= 1) : xi+1 = ( s / ( 4 (1 - d) ) ) (1 - xi)

if (d < 0.5) :
0 <= s <= 2

else if (d >= 0.5) :
0 <= s <= 4

Ginger Booth for Michael Frame, March 2005