Fractal Geometry of Nature

[Racoon]

Turtle did something stupid, and gave Racoon a book;
It just sat on the shelf, until Geometry overtook!!..............

The Fractal Geometry of Nature.

What is a Koch Pyramid?

Poincares remark that " there are questions that one chooses to ask and other questions that ask themselves "....

FRACTAL is a word invented by Mandelbrot to bring together under on heading a large class of objects that have [played]... an historical role... in the development of pure Mathmatics"....

Heres the discussion point: Dimension, Symmetry, and Dirvegence found in nature to have mathmatical principles behind them...

It talks about Euclidean Stuff...

Says " The homogenous distribution on a line, plane, or space has two very desirable properties. It is invariant under displacement, and it is invariant under change of scale. When we move on to Fractals, either invariance must be modified and/or restricted in its scope. Hence the best fractals are those that exhibit the Maximum of invariance."

Lots of formulas my keyboard won't type.

Anyone have any ideas on Geometric function found in Nature?
How leaves form a uniform pattern, usually??

The Book I am Referring to is called " The Fractal Geometry of Nature" by Mandelbrot; Published by Freeman and co. New York, originally in 1977 and this copy is 1983...

Talks about Math related to:
>Galaxies and Eddies
> Scaling
> Self- mapping
> Randomness
> Stratified random
> logic of Fractals in Statistical Lattice Physics
> Random midpoint Displacement curves

and a whole lot more......

My Math level is College Algebra. I haven't had any Calculus..
So I am asking the boundry-less brains of this forum...

[Racoon]

30 views and no reply?

I guess nobody gives a rip.
This book could be bogus.
Its all Turtle's fault!

OK, heres a little more to Slake your Thirst...

The Koch curve:for coastlines and such
the Dimension D = log^4 / log^3 ~1.2618>1

ah screw it!

If my keyboard could type up some of these equations, then it could be beaten up by the Math Whizzes we got running around this site!

Do any of these things ring a bell??

>Self-Inverse Fractals, Apollonian Nets?
> Chance as a tool in Model Making
> Conditional Stationarity and Cosmographic Principles
> Random Chains and Squigs
> Brownian Motion
> Interval Tremas; Linear Levy Dusts
> Subordination; Spatial Levy Dusts; Ordered Galaxies
> yada yada yada...

I hear crickets

[InfiniteNow]

Sorry Rac... I don't know too much about the question personally. Your post did remind me of a thin little book I read several years ago called "The Geometry of Art and Life." That was cool. Spoke of the Golden spiral/rectangle a lot...

[Racoon]

Originally Posted by InfiniteNow

Sorry Rac... I don't know too much about the question personally. Your post did remind me of a thin little book I read several years ago called "The Geometry of Art and Life." That was cool. Spoke of the Golden spiral/rectangle a lot...

I guess thats why I stick to 'softer' science...
Except Chemistry. Although I am a little soft in It.

heres one I found I could type:

Sample standard deviation of X(t),
S^2(d) = X^2*(d) / d - X*^2(d) / d^2

This book isn't really making sense to me.

ps. Nice HStaff you're sportin' there IN!

[InfiniteNow]

Don't be too hard on yourself. Often it's not the concept that eludes you, but the inability of the author to explain it adequately. Maybe try a book on the same topic by another author. That might just turn things around as far as your understanding is concerned...


Cheers.

[Turtle]

Originally Posted by Racoon

30 views and no reply?

I guess nobody gives a rip.
This book could be bogus.
Its all Turtle's fault!

OK, heres a little more to Slake your Thirst...

The Koch curve:for coastlines and such
the Dimension D = log^4 / log^3 ~1.2618>1

I hear crickets

___Few give a rip, not nobody gives a rip.
___Any book could be bogus; reader beware.
___It is not my fault, I am the fault; cracked Earth, get it.
___The book is the seminal work describing and literally defining 'fractal'. Never mind if you understand the text & formulae, just read it, front to back while enjoying the pretty pictures & drawings. Let the general sense of the work soak in like the steady new waves lapping a sandy shore.
___Because with this new understanding of dimension, that is we have not just 2-dimensional thingys, & 3-dimensional thingys, but 1.2618 dimensional thingys & so on in between, and because they pervade nature, and because they share recursion as an operative element, I think any real grand unified theory must include recursion as an operative element.
___Pretty pictures...pretty pictures...

[Racoon]

Originally Posted by Turtle

___The book is the seminal work describing and literally defining 'fractal'. Never mind if you understand the text & formulae, just read it, front to back while enjoying the pretty pictures & drawings.

Oh
I've been reading it back to front!

Ok, mostly looking at the Pretty Pictures

[TheBigDog]

Didn't Mandelbrot develop the theory from studying details in the charts of sheep futures? I have fractal screen saves on all my computers. I think they are beautiful.

Bill

[Racoon]

What can you say about Mandelbrot??

Dude knew his Fractals.........??

[Qfwfq]

Haven't you folk learnt to delete posts properly?