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IFS_2d
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1996-10-09
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IFS 2d: An implementation of Michael Barnsley's IFS system in 2 dimensions.
------
Up to 40 IFS transformations are stored internally, one of which is the
working IFS.
IFS plots points, the colours of which are set from the main Plot Options
dialogue box in the Effects menu.
From the IFS menu the options are:
Data: The current IFS data except for the zooming co-ordinates which are
accessed via the standard Image⇨Data⇨ menu. Click Input to enter new values,
or Re-draw to enter and re-draw the image. Click Store to store the data in
the internal file, or Restore to revert to the version held internally.
Click Copy to take a copy of the current data and create a new IFS function,
or click Delete to delete the current entry.
The data on display consists of:
Name: used to identify the IFS function, any 1-11 characters.
Number: location within the internal IFS file. Click on the arrows to access
prior or next entries.
Transformations: number of affine transforms to use (1-20). If the sum of
the probabilities is less than 1, this number is automatically increased by
1 and a null transformation is added.
Iterations: The number of iterations before stopping image generation.
The affine data is shown according to its place in the affine function, not
as a,b,c... as shown in some programs, so be careful when porting values.
The sum of the probabilties must be >=1. If not, an extra null
transformation is added. To move around the grid use !Fractal's standard
editing keys. Numbers may be entered in scientific format. Remember to click
Input or Re-draw afterwards to get the new values processed. Only the first
9 values are shown. If a function has more (such as Chaos) then use !Edit to
edit the IFS data file & reload into Fractal.
List: shows a panel listing all the internal IFS functions available. Click
over a name to make it the current one. Most of these came from Fractint, so
see there for credits.
Save: allows the internal IFS file to be saved as a text file. Saved files
can be re-loaded by dragging onto the !Fractal icon or window. Please send
in exciting new IFS functions to AFG so that we may all see them.
Algorithm
---------
The algorithm to generate each point is essentially as shown on the input
panel, ie:
r=random number from 0 to 1
select affine transformation whose probability sum is just less than r
x=a*x+b*y+c
y=d*x+e*y+f
plot x,y
where a..f refer to the columns in the data input panel left to right.