Arthur C. Clarke, Fractals: Colors of infinity

[Nowhere]

Remember that series Arthur C. Clarke's World of Strange Powers? One was about fractals. And it featured a magnificent example of fractal zooming in of the parrot picture. I want to play with this!!! (even if, as I assume, usually results aren't so astonishing - it resembles original at best).
Does any of you has any info about the (or such) software?

[Nowhere]

Found some info...

In it, the developer/owner of Iterated Systems was interviewed. During his
interview there was a demonstration of a software filter which was
used on a severely data reduced (pixelated) image of a part of a
parrots eye.

Michael Barnsely (the developer/owner) has written a book called "Fractals
Everywhere" that covers the ground you're interested in. Iterated Systems
has since bought algorithms for other extremely high data compression
methods (weighted finite automata, etc.).

Still...not enough for me