---------------- home Balloting Simple trig Logistic Difference Equation The Attractor of Henon Number doubling Barnsley's Fern The Sierpinski TriangleThe Attractor of HenonX = ((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 ============================================================= home Balloting Simple trig Logistic Difference Equation The Attractor of Henon Number doubling Barnsley's Fern The Sierpinski Triangle