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Naturally Occurring Fractals

(including plants, rivers, galaxies, clouds, weather, population patterns, stocks, video feedback, crystal growth, etc.)

fractals in natureThe 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 fren iteration

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 surprising too!
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
fractal mountains and coastline       Fractal Rivers
             Mandelbrot set area displaying dendritic branching like river erosion patterns
fractal landscape         mandelbrot natural branching

  
     Fractal Growth Pattern of a Leaf                                             Chaotic Fractal Branching Pattern from Electrical Discharge

Fractal leaf veins       electrical Fractal

Edible Fractals: Romanesco (a cross between broccoli and Cauliflower, which accentuates the great fractal spiral patterns on the top. Tastes a-ok too)
Fractal Patterns in a Hydrothermal Spring
fractal romanesco
fractal water flow


Natural Fractal Landscape:
this view of valleys and river basins displays beautiful capillary fractal dendritic branching.

Digital Fractal Landscape made of 100% Math

Mountains & Pastures by "ostrich"
fractal landscape
fractal landscape

Natural Cloud Spiral Fractals
photograph, not digital

mathematical generated landscape

Fractally Generated lanscape
- tranquil snow-capped mountains

mathematical generated landscape

Natural Cloud Spiral Fractals photograph, not digital
mathematical generated landscape
Mandelbrot Set 'Saehorse valley' with similar swirls
mathematical generated landscape

Natural Cloud Fractals
photograph, not digital

mathematical generated landscape

Fractally Generated lanscape
resembling windswept sandstone

mathematical generated landscape
   

Natural Fractals are visible in these landscapes painted by Maxfield Parish (1870--1966)
fractal landscape    fractal landscape


Below:
Fractal Electric Discharge Patterns Generated by
Placing a CD into a Microwave for approximately 4 seconds!!

fractal cd burn


Lightning Strikes and Electrical Discharge creates fractal formations
called Lichtenberg figures on rocks, grass,wood or even people!
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
electrical fractal      fractal burn from a lightening strike
Lichtenberg Figures on a Patient Due to a Lightning Strike
by Yves Domart, MD, and Emmanuel Garet, MD,







3D FRACTALS
Familiar Forms
; looking like waterspouts, roots, clouds, and dragons.
to the LEFT we see a simulated Oceanic-Scene with Fractal Seaweed and
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
haeckel fractal
haeckel fractal

Cut into a Cabbage and you'll find a Fractal - Inside of a thin cross-section of wood stalk there is a circular Fractal
fractal cabbage   Fractal plant cells



BELOW:
Virus, mold and bacterial aggregate colonies spontaneously assume Fractal Shapes
(from Science News)
fractal bacteria, mold and colonies

fractal bacteria, mold and colonies

fractal bacteria, mold and colonies


fractal bacteria, mold and colonies

fractal bacteria, mold and colonies



Check Back Soon For Updates!


An Introduction to the Fascinating Patterns of Chaos & Visual Math
Platonic & Vectoral Geometry Simple Iterative Fractals Natural fractals
Multi Dimensional Forms The Famous Mandelbrot Set Fractal Types & Categories
PHI - the Golden Ratio Mandelbulb & 3 Dimensional Fractals Fractal "Wada" Basin Reflections
Minimal Surfaces Fractal Technology & Historical Fractals Other Fractals & Cool Patterns


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Fractal Art Image Gallery
Fractal Art Image Gallery



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