Wonderful World of Gnarls

Head over Heels

Dance of the Cobra

When the Dog Gnarls

Gee up Gnarlie

Carousel of Gnarls

Be an Animal

Snap Crackle Pop and Gnarl

Gnarly Fountain

Playing with Fire

Images are copyrighted by international law.
Use of any image in any way without written
permission of the owner is strictly prohibited.
All images © Amorina Ashton 2007-2008.

Gnarl

Today i want to show a type of fractal called Gnarl.

Noun
Singular - gnarl
Plural - gnarls

1. a knot in wood; a large or hard knot, or a protuberance with twisted grain, on a tree.
2. something resembling a knot in wood, such as in stone or limbs.

Verb
Infinitive - to gnarl
Third person singular - gnarls
Simple past - gnarled
Past participle - gnarled
Present participle - gnarling

1. (transitive) to knot or twist something
2. (intransitive) to snarl or growl; to gnar

but in mathematics, and also in Fractals it means:-
The average value of the magnitude squared of the curl of a vector field over a continuous path that is tangent to the vector field at every point. In mathematical notation, gnarl is represented by the lowercase Greek letter ξ.

Or to put it simply, twisted, knotted, deformed.

Resources:-
http://en.wiktionary.org/wiki/gnarl http://www.thefreedictionary.com/gnarl

In FractalArt the knots look like eyes sometimes and can make for some very funny pictures as you will see in my next post.
Enjoy my Fractal World of Gnarls :-)

A Taste of my Fractals

Carvings of a Totem Pole

Silken Secrets

Make a Decision

Those Stars

DeLIGHTful

Wings upon Wings

The Orange One

Garden of Spirals

Images are copyrighted by international law.
Use of any image in any way without written
permission of the owner is strictly prohibited.
All images © Amorina Ashton 2007-2008.

Definitions of a Fractal

For those of you who don't know:-

FRACTAL –noun Mathematics, Physics.
a geometrical or physical structure having an irregular or fragmented shape at all scales of measurement between a greatest and smallest scale such that certain mathematical or physical properties of the structure, as the perimeter of a curve or the flow rate in a porous medium, behave as if the dimensions of the structure (fractal dimensions) are greater than the spatial dimensions.

[Origin: < F fractale, equiv. to L frāct(us) broken, uneven (see fractus) + -ale -al2; term introduced by French mathematician Benoit Mandelbrot (born 1924) in 1975]

[1] fractal. (n.d.). Dictionary.com Unabridged (v 1.1). Retrieved November 18, 2008, from Dictionary.com website: [link]


FRACTAL-n. A geometric pattern that is repeated at ever smaller scales to produce irregular shapes and surfaces that cannot be represented by classical geometry. Fractals are used especially in computer modeling of irregular patterns and structures in nature.

[French, from Latin frāctus, past participle of frangere, to break; see fraction.]

The American Heritage® Dictionary of the English Language, Fourth Edition
Copyright © 2006 by Houghton Mifflin Company.
Published by Houghton Mifflin Company. All rights reserved.


FRACTAL- mathematics, graphics
A fractal is a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a smaller copy of the whole. Fractals are generally self-similar (bits look like the whole) and independent of scale (they look similar, no matter how close you zoom in).

Many mathematical structures are fractals; e.g. Sierpinski triangle, Koch snowflake, Peano curve, Mandelbrot set and Lorenz attractor. Fractals also describe many real-world objects that do not have simple geometric shapes, such as clouds, mountains, turbulence, and coastlines.
Benoit Mandelbrot, the discoverer of the Mandelbrot set, coined the term "fractal" in 1975 from the Latin fractus or "to break".

The Free On-line Dictionary of Computing, © 1993-2007 Denis Howe