plants, rivers, galaxies, clouds, weather, population
patterns, stocks, video feedback, crystal growth, etc.)
geometry of Fractals brings us a new appreciation for
the natural world
and the patterns we observe in it.
Many things previously called chaos are now known
to follow subtle subtle fractal laws of behavior. So many
things turned out to be fractal that the word "chaos"
itself (in operational science) had redefined, or actually
for the FIRST time Formally Defined as following
inherently unpredictable yet generally deterministic rules
based on nonlinear iterative equations. Fractals
are unpredictable in specific details yet deterministic
when viewed as a total pattern - in many ways this reflects
what we observe in the small details & total pattern
of life in all it's physical and mental varieties, too
FRACTAL FERN: One very simple way to understand fractals
and the meaning of "lteration" is to examine
a simple recursive operation that produces a fractal fern
thru a "chaos game' of generating random numbers
and then placing them on a grid.
After a few dozen repetitions or ITERATIONS the shape
we would recognize as a Perfect Fern appears from the
abstract world of math.
How and Why can this be?
The answer to why is that it Simply IS - and it's quite
Answering How is that nature always follows the simplest
& most efficient path. Fractals are maps of the simplest
paths sliding up the scale of Dimensions (from 2-D to
3-D and so on). So maybe it's simply an artifact of nature's
elegance that we find exact correspondences between these
inherently existing mathematical forms and natural patterns,
and even living creatures of many types.
Fractals in nature are ubiquitous - clouds, plants, galaxies, shells and more.
| Fractal Mountains In Tibet Fractal Rivers in Savannah, Georgia
Mandelbrot set area displaying dendritic branching like river erosion patterns
Fractal Growth Pattern of a Leaf Chaotic Fractal Branching Pattern from Electrical Discharge
Natural Fractals are visible in these landscapes painted by Maxfield Parish (1870--1966)
Below: Fractal Electric Discharge Patterns Generated by
Placing a CD into a Microwave for approximately 4 seconds!!
Lightning Strikes and Electrical Discharge creates fractal
called Lichtenberg figures on rocks, grass,wood or even
From Tennessee's Oak-Ridge Laboratory Museum "This particular Lichtenberg Figure was created by
exposing a rotating lucite cylinder to the electron beam.
When the cylinder was discharged by striking one end with
a grounded rod, the electrons created a three dimensional
Lichtenberg Figure. Size: 12.5 " long, 2" diameter
Lichtenberg Figures on a Patient Due to a Lightning Strike
by Yves Domart, MD, and Emmanuel Garet, MD,
Familiar Forms; looking like waterspouts,
roots, clouds, and dragons.
to the LEFT we see a simulated Oceanic-Scene with Fractal
Coral composed from 3-d rendered IFS fractals.
Below we see more amazing quaternion 4-D julia sets.
Ernst Haeckel drawings of Fractal Life Forms from the sea
Cut into a Cabbage and you'll find a Fractal - Inside of a thin cross-section of wood stalk there is a circular Fractal
Virus, mold and bacterial aggregate colonies spontaneously
assume Fractal Shapes
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Fractal Art Image Gallery
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