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Henon
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1996-10-09
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Hénon Maps : An implementation of Hénon's strange attractor.
----------
Two sub-functions are provided. The Original function shows a simple orbit,
whilst the SIN/COS function is a fuller implementation. They both relate to
orbits of asteroids and so on.
Henon plots points, the colours of which are set from the main Plot Options
dialogue box in the Effects menu.
The menu options are greyed when not applicable to a particular function.
The menu options are:
Original: selects the basic function. This function is infinite so you will
need to manually stop it. See Chaos by J.Gleick p.141 for full details.
SIN(a)/COS(a): selects the full function. See J.Dewdney, Sc.American, July
1987.
Random a: The value of a is chosen at random by the program when ticked.
Random b: The value of a is chosen at random by the program when ticked.
Auto Step: When on, the number of points calculated will be increased as you
zoom in, to give greater resolution, though this will take longer.
Original Algorithm:
------------------
The default value for a is 1.4 and b is 0.3. The best
results come from slightly altering these values rather than choosing random
figures.
px=1
py=1
do
z=px
px=py+1-a*z*z
py=b*z
plot px,py
until (x>1.0e10 or y>1.0e10)
SIN(a)/COS(a) Algorithm:
-----------------------
Here the main control is the data variable a. The step rate is decreased
when zooming in. Thanks to Joyce Haslam for passing on this algorithm.
for i=-0.8 to 0.8 step 0.05
for j=-0.8 to 0.8 step 0.05
c=0; x=i; y=j
repeat
c+=1
xx=x*COSa-(y-x*x)*SINa
y=x*SINa+(y-x*x)*COSa
x=xx
plot x,y
until (i>100 or x>1000 or y>1000)
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