Re: ifs image width and height

In message <1157129919.393044.257280@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>, marcosd@xxxxxxxxx writes
Hello there!

Is there some way to predict the width and height of an IFS attractor?
My programs generating IFS images always make some iterations to store
the maximal and minimal x and y coordinates... Wich is some
cumbersome...

I do the same.

Is there another way?

Regards


Sometimes you can find an extremum by repeatedly tranforming using one transform, but this doesn't necessarily work when rotations and reflections are involved.

You could try exploiting the Xerox algorithm. Pick a rectangle of the appropriate aspect ratio which you are sure includes the whole of the attractor. (Ten times larger than the largest translation involved would seem to be more than adequate.) Transform the four corners of this rectangle with each transform, and find the smallest rectangle which includes all the points so obtained. Repeat until the reduction in size of the rectangle is less than some threshold.
--
Stewart Robert Hinsley
.

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