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Lorenz
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1996-10-09
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Lorenz : The Edward Lorenz Strange Attractor.
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This was probably the first fractal to be recognised as such, and started
the ball rolling for chaos investigation. The shape is three dimensional and
you can use !Fractal's rotation and elevation icons to control the view
position. There are three variables which may be set or randomly chosen, and
there are three colour schemes. Refer to Chaos by J.Gleick for a description
of the story behind its discovery.
The plot is infinite. You can control the speed by setting the Step Rate
factor - smaller values will slow the plot so you can trace its shape.
Notice that the plot revolves around one centre and then suddenly jumps
across to the other. Try altering the default values of a/b/c by small
amounts and see the effect this has on the shape and when the jump occurs.
The menu options are:
Random a/b/c: Click to set/unset random selection of the variable when a
plot is started. For each variable there is an associated maximum, which can
be changed from the data panel. New variables are not chosen when zooming.
Once you have found an interesting shape, turn off random variables, and use
the 3d options to explore the shape.
Random colour: when set a random colour is chosen after every 100 plots.
Step Colour: the colour value is increased after every 100 plots.
If neither Random or Step colour is set, then the plot is made in white
using exclusive or'ing to trace the current position.
You can change the viewpoint whilst plotting by pressing the cursor keys,
and then pressing the space bar to restart. See the 3d section in the
!MainHelp file for more details. Try Step Rate=2.0e-2 for the best use of
this function - note that bigger values destroy the shape.
Algorithm
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x=1; y=1; z=1;
do forever
dx=a*(py-px)
dy=px*(b-pz)-py
dz=px*py-c*pz
px+=dx*step_rate
py+=dy*step_rate
pz+=dz*step_rate
draw px,pz where px/pz are 3d transforms of x/y/z
enddo