scripts/alpaca60 Arneodo.LACE

   1 # Arneodo-Attractor (alpaca_60)
   2 # x' = y, x0 = 1
   3 # y' = z, y0 = 1
   4 # z' = a*x-b*y-z-c*x^3, z0=0
   5 # a=5,5; b=3,5; c=1
   6 #
   7 # SCALING
   8 # the problem is patched as designed, but x runs out of range
   9 # Trial: x = 5*xn (xn = new x), y = 10*yn, z = 15*zn
  10 #    5*xn' = 10*y                              => xn' = 2*y
  11 #    10*y' = 15*zn                             => y'  = 1,5*z
  12 #    15*zn' = a*5*xn-b*10*yn-15*zn-c*(5*xn)^3  => z' = a*5/15*xn-b*10/15*yn-15/15*zn-c*125/15*xn^3
  13 #
  14 #    xn' = d1*y
  15 #    yn' = e1*z
  16 #    zn' = a1*xn-b1*yn-zn-c1*xn^3
  17 #
  18 #    a1 = a*5/15 = 1,83
  19 #    b1 = b*10/15 = 2,33
  20 #    c1 = c*5^3/15 = 8,33
  21 #    d1 = 2
  22 #    e1 = 1,5
  23 #
  24 # in the following, the original terms are being used,
  25
  26 coefficient.1     -> a/10 # 0,183 -> better results with 0,154
  27 coefficient.2     -> b/10 # 0,233
  28 coefficient.3     -> c/10 # 0,833
  29 coefficient.4(+1) -> x0   # 0,200
  30 coefficient.5(+1) -> y0   # 0,100
  31 coefficient.6(+1) -> z0   # 0
  32 coefficient.7     -> d/10 # 0,200
  33 coefficient.8     -> e/10 # 0,150
  34
  35 iintegrate 10*: x' -> -x
  36   IC: x0
  37 iintegrate 10*: y' -> -y
  38   IC: y0
  39 iintegrate z' -> -z
  40   IC: z0
  41
  42 invert -x -> x
  43
  44 invert -y -> y
  45 cmultiply y, d/10 -> d/10*y
  46 assign d/10*y -> x'
  47
  48 invert -z -> z
  49 cmultiply z, e/10 -> e/10*z
  50 assign e/10*z -> y'
  51
  52 cmultiply x, a/10 -> a/10*x
  53 cmultiply -y, b/10 -> -b/10*y
  54
  55 multiply -x, -x -> x^2
  56 multiply x^2, -x -> -x^3
  57 cmultiply -x^3, c/10 -> -c/10*x^3
  58
  59 isum 10*:a/10*x, 10*:-b/10*y, -z, 10*:-c/10*x^3 -> -(a*x-b*y-z-c*x^3)
  60 invert -(a*x-b*y-z-c*x^3) -> a*x-b*y-z-c*x^3
  61 assign a*x-b*y-z-c*x^3 -> z'
  62
  63 output x -> out.x
  64 output y -> out.y
  65 output z -> out.z