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Balloting

Simple trig

Logistic map

The Attractor of Henon

Number doubling

Barnsley's Fern

The Sierpinski Triangle


The Attractor of Henon


      X = ((previousY + 1) - (1.4 * previousX ^ 2))
      Y = (0.3 * previousX)  

      Iterating this pair of equations produces a strange
      simple set of curved lines that is poorly understood 
      by mathematicians.  As thousands, then millions of
      points appear, more and more detail emerges.  What 
      appear to be single lines prove, on magnification, 
      to be pairs, then pairs of pairs, and so on to
      infinity.  Whether any two successive points appear 
      nearby or far apart is unpredictable.


I used .3, .2 as initial values for X, Y 
(built into the program code)

Start with iterations = 20, 

then 60,
then 100, 
then 200,
then 400, 
then 800, 
then 1500, 
then 3000, 
then 10000
then 20000
then 40000
then 100000

watching the strange attractor slowly materialize.





For fun, the attractor superimposed onto a starfield
(the "double a number" algorithm)





VisualBASIC program code:


Private Sub attractorbtn_Click()

ITER = Val(itera.Text)

OLDX = 0.3: OLDY = 0.2

For ATTR = 1 To ITER

   X = ((OLDY + 1) - (1.4 * OLDX ^ 2))
   Y = (0.3 * OLDX)

   TEMPX = (260 * X) + 430
   TEMPY = (260 * Y) + 530

   viewport.PSet (TEMPX, TEMPY), RGB(208, 32, 6)

   OLDX = X
   OLDY = Y

Next ATTR

End Sub

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home


Balloting

Simple trig

Logistic map

The Attractor of Henon

Number doubling

Barnsley's Fern

The Sierpinski Triangle