This Java applet was originally made in 2001. Something amazing happened in 2004.
Don Hatch saw my applet on the Internet and
he spend some effort to improve the features. My initial program can only do the
even number iternations. Don Hatch made it work from 0 to 13. Many thanks to
Don's generous offer to use his program.
Here is a description by Hans Lauwerier "Fractals are shapes in which an identical
motif repeats itself on an ever diminishing scale". Most fractal images are
complex in appearance and will not fit together. Dr. Fathauer showed lots of
fractal tiles that fit together.
The tile shrinks in size as you progress out from a nucleus. The tiles
are similar and the pattern has rotation symmetry.
The fractal tiles shown here, Koch Island and Twin Dragon, are periodic tiles
with translational symmetry.
The fractal properties make the boundary features shrink in size and become
more complex. But the tile retains the same area and fits together with
Julia fractals caught a lot of attention because the graphics is spectacular.
It was discovered 80 years ago by Gaston Julia without the use of computer or
image. The paper was forgotten for 50 years because it had no
illustrations. It was brought back into the public attention by Mandelbrot
and computer graphics really gave it life.
This fractal tiling is suitable for building decoration and interior design.
This Twin Dragon looks good with 1 inch square tiles on a bath enclosure.
Look at David Chow's interpretation of the Twin Dragon