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The fern

A random number  r is generated   0  ≤ r ≤ 1

Start with x=0.5 and y= 0.0,  and use the linear equations:

     if  r < A                  xn = 0.5,                                        yn = 0.27*y;

     if  r>A  and  r ≤  B    xn = -0.139*x + 0.263*y + 0.57,   yn = 0.246*x + 0.224*y - 0.036

     if  r>B   and  r ≤  C    xn = 0.17*x - 0.215*y + 0.408,     yn = 0.222*x + 0.176*y + 0.0893

     else                          xn = 0.781*x + 0.034*y + 0.1075,  yn = -0.032*x + 0.739*y + 0.27

To see the effects of changing the probabilities for the equations:

Select A  with west slider (see equations)

Select B with east slider

Select C with north slider

And press start to see the new fern.