name Fractiles is a combination of the word "fractal",
meaning the phenomenon of scaling or the repeating
of a pattern on every scale - and the word "tiles".
is a relatively new word, yet it describes
something which we recognize intuitively.
Fractal refers to a geometric shape that is
complex and detailed, yet similar at any level
of magnification. Examples include a rugged
coastline which when seen from space becomes
ever more complex as the viewer moves closer.
Coastlines turn into rugged boulders, then
into sand, and then finally into sub-atomic
particles. Yet at every level of magnification
the pattern is similar.
Benoit Mandelbrot called those shapes
"fractals". He also wrote that fractals
are "self-similar" meaning that each
portion of a fractal can be viewed as
a smaller replica of the whole. If you
look closely at a fern, for example,
you will see the same pattern reproduced
at every level. The leaves seem to be
made up of miniature ferns - repeating
the shape of the whole in ever decreasing
live in a fractal Universe. Our Sun is just
one star among billions of stars which make
up our Milky Way Galaxy. The Milky Way Galaxy
is merely a tiny part of a super galaxy (a
galaxy made of galaxies). In the vast expanse
of celestial space, a super galaxy is but
a tiny replicated part of a super-super galaxy,
Large Boulders |Similarly,
when we zoom in on the world of sub-atomic
particles, we find that it is composed of
endlessly smaller structures within structures,
all of which have similarity of pattern. There
is no known limit to how large or small fractals
can be. We humans are somewhere on an endless
call the similarity of pattern which exists
everywhere from the infinitesimal to the unimaginably
vast - the "fingerprint of God".
Sand Magnified |The
spiritual insight that the Universe is a fractal
transforms this earthly world into one of
splendour and mutual fusion.
see the World in a grain of Sand
And Heaven in a wild Flower
Hold Infinity in the palm of your hand
And Eternity in an hour.