By Damon Hellandbrand
Aries
Taurus
Gemini
Cancer
Leo
Virgo
Libra
Scorpio
Sagittarius
Capricorn
Aquarius
Pisces
Thursday, January 15, 2015
Wednesday, August 6, 2014
Tuesday, March 12, 2013
Into the infinite
A fractal is a mathematical set that has a fractal dimension that usually exceeds its topological dimension and may fall between the integers. Fractals are typically self-similar patterns, where self-similar means they are "the same from near as from far". Fractals may be exactly the same at every scale or they may be nearly the same at different scales. The definition of fractal goes beyond self-similarity per se to exclude trivial self-similarity and include the idea of a detailed pattern repeating itself.
As mathematical equations, fractals are usually nowhere differentiable. An infinite fractal curve can be perceived of as winding through space differently from an ordinary line, still being a 1-dimensional line yet having a fractal dimension indicating it also resembles a surface.
The mathematical roots of the idea of fractals have been traced through a formal path of published works, starting in the 17th century with notions of recursion, then moving through increasingly rigorous mathematical treatment of the concept to the study of continuous but not differentiable functions in the 19th century, and on to the coining of the word fractal in the 20th century with a subsequent burgeoning of interest in fractals and computer-based modelling in the 21st century.The term "fractal" was first used by mathematician Benoît Mandelbrot in 1975. Mandelbrot based it on the Latin frāctus meaning "broken" or "fractured", and used it to extend the concept of theoretical fractional dimensions to geometric patterns in nature.
There is some disagreement amongst authorities about how the concept of a fractal should be formally defined. The general consensus is that theoretical fractals are infinitely self-similar, iterated, and detailed mathematical constructs having fractal dimensions, of which many examples have been formulated and studied in great depth. Fractals are not limited to geometric patterns, but can also describe processes in time. Fractal patterns with various degrees of self-similarity have been rendered or studied in images, structures and sounds and found in nature, technology, art, and law.
- http://en.wikipedia.org/wiki/Fractal
As mathematical equations, fractals are usually nowhere differentiable. An infinite fractal curve can be perceived of as winding through space differently from an ordinary line, still being a 1-dimensional line yet having a fractal dimension indicating it also resembles a surface.
The mathematical roots of the idea of fractals have been traced through a formal path of published works, starting in the 17th century with notions of recursion, then moving through increasingly rigorous mathematical treatment of the concept to the study of continuous but not differentiable functions in the 19th century, and on to the coining of the word fractal in the 20th century with a subsequent burgeoning of interest in fractals and computer-based modelling in the 21st century.The term "fractal" was first used by mathematician Benoît Mandelbrot in 1975. Mandelbrot based it on the Latin frāctus meaning "broken" or "fractured", and used it to extend the concept of theoretical fractional dimensions to geometric patterns in nature.
There is some disagreement amongst authorities about how the concept of a fractal should be formally defined. The general consensus is that theoretical fractals are infinitely self-similar, iterated, and detailed mathematical constructs having fractal dimensions, of which many examples have been formulated and studied in great depth. Fractals are not limited to geometric patterns, but can also describe processes in time. Fractal patterns with various degrees of self-similarity have been rendered or studied in images, structures and sounds and found in nature, technology, art, and law.
- http://en.wikipedia.org/wiki/Fractal
Monday, February 18, 2013
Thursday, December 6, 2012
My absence of original thought
"It's a mistake to think that people change. But it's a bigger mistake to think people can't." - Umair Haque
"I'm not in this world to live up to your expectations and you're not in this world to live up to mine."
-Bruce Lee
"Under capitalism man exploits man. Under communism it is just the reverse." - Henry Shapiro
"Any one who has common sense will remember that the bewilderments of the eyes are of two kinds, and arise from two causes, either from coming out of the light or from going into the light, which is true of the mind's eye, quite as much as of the bodily eye; and he who remembers this when he sees any one whose vision is perplexed and weak, will not be too ready to laugh; he will first ask whether that soul of man has come out of the brighter light, and is unable to see because unaccustomed to the dark, or having turned from darkness to the day is dazzled by excess of light." - Plato
"The glass I drink from is not large, but at least it is my own." -Alfred de Musset
"It is hard enough to remember my opinions, without also remembering my reasons for them!" - Friedrich Nietzche
"He who knows when he can fight and when he cannot will be victorious." - Sun Tzu
"I'm so excited, I can't wait to meet you there, And I don't care." - Nirvana
"A facility for quotation covers the absence of original thought." - Dorothy L. Sayers
"I never did give them hell. I just told the truth, and they thought it was hell." - Harry S Truman
"This source of corruption, alas, is inherent in the democratic system itself, and it can only be controlled, if at all, by finding ways to encourage legislators to subordinate ambition to principle." - James L. Buckley
"Democracy consists of choosing your dictators, after they've told you what you think it is you want to hear." - Alan Corenk
"Find my nest of salt... Everything is my fault..." - Nirvana
"Anyone can win unless there happens to be a second entry." - George Ade
"Imagination was given to man to compensate him for what he is not; a sense of humor to console him for what he is." - Francis Bacon
"A slip of the foot you may soon recover, but a slip of the tongue you may never get over." - Benjamin Franklin
"Whatever you do will be insignificant, but it is very important that you do it." - Mahatma Gandhi
"I am not bound to please thee with my answers." - William Shakespeare
"The visionary lies to himself, the liar only to others." - Friedrich Nietzche
"We lie the loudest when we lie to ourselves." -Eric Hoffer
"All that we see or seem is but a dream within a dream." - Edgar Allan Poe
"Three things can not hide for long: the Moon, the Sun and the Truth." – Siddhartha
"I never think about the future, it comes soon enough." - Albert Einstein
"The future will be better tomorrow." - Dan Quayle
"The advantage of a bad memory is that one enjoys several times the same good things for the first time." - Friedrich Nietzsche
"The successful revolutionary is a statesman, the unsuccessful one a criminal." - Erich Fromm
"I want freedom for the full expression of my personality." - Mahatma Gandhi
"Never to suffer would never to have been blessed." - Edgar Allan Poe
"It is pretty hard to tell what does bring happiness; poverty and wealth have both failed." - Kin Hubbard
"Imagination is more important than knowledge..." - Albert Einstein
"Education is a progressive discovery of our own ignorance." - Will Durant
"One's first step in wisdom is to question everything - and one's last is to come to terms with everything." - Georg Christoph Lichtenberg
"There is no revenge so complete as forgiveness." - Josh Billings
"Kindness is more important than wisdom, and the recognition of this is the beginning of wisdom." -Theodore Rubin
"I'm not in this world to live up to your expectations and you're not in this world to live up to mine."
-Bruce Lee
"Under capitalism man exploits man. Under communism it is just the reverse." - Henry Shapiro
"Any one who has common sense will remember that the bewilderments of the eyes are of two kinds, and arise from two causes, either from coming out of the light or from going into the light, which is true of the mind's eye, quite as much as of the bodily eye; and he who remembers this when he sees any one whose vision is perplexed and weak, will not be too ready to laugh; he will first ask whether that soul of man has come out of the brighter light, and is unable to see because unaccustomed to the dark, or having turned from darkness to the day is dazzled by excess of light." - Plato
"The glass I drink from is not large, but at least it is my own." -Alfred de Musset
"It is hard enough to remember my opinions, without also remembering my reasons for them!" - Friedrich Nietzche
"He who knows when he can fight and when he cannot will be victorious." - Sun Tzu
"I'm so excited, I can't wait to meet you there, And I don't care." - Nirvana
"A facility for quotation covers the absence of original thought." - Dorothy L. Sayers
"I never did give them hell. I just told the truth, and they thought it was hell." - Harry S Truman
"This source of corruption, alas, is inherent in the democratic system itself, and it can only be controlled, if at all, by finding ways to encourage legislators to subordinate ambition to principle." - James L. Buckley
"Democracy consists of choosing your dictators, after they've told you what you think it is you want to hear." - Alan Corenk
"Find my nest of salt... Everything is my fault..." - Nirvana
"Anyone can win unless there happens to be a second entry." - George Ade
"Imagination was given to man to compensate him for what he is not; a sense of humor to console him for what he is." - Francis Bacon
"A slip of the foot you may soon recover, but a slip of the tongue you may never get over." - Benjamin Franklin
"Whatever you do will be insignificant, but it is very important that you do it." - Mahatma Gandhi
"I am not bound to please thee with my answers." - William Shakespeare
"The visionary lies to himself, the liar only to others." - Friedrich Nietzche
"We lie the loudest when we lie to ourselves." -Eric Hoffer
"All that we see or seem is but a dream within a dream." - Edgar Allan Poe
"Three things can not hide for long: the Moon, the Sun and the Truth." – Siddhartha
"I never think about the future, it comes soon enough." - Albert Einstein
"The future will be better tomorrow." - Dan Quayle
"The advantage of a bad memory is that one enjoys several times the same good things for the first time." - Friedrich Nietzsche
"The successful revolutionary is a statesman, the unsuccessful one a criminal." - Erich Fromm
"I want freedom for the full expression of my personality." - Mahatma Gandhi
"Never to suffer would never to have been blessed." - Edgar Allan Poe
"It is pretty hard to tell what does bring happiness; poverty and wealth have both failed." - Kin Hubbard
"Imagination is more important than knowledge..." - Albert Einstein
"Education is a progressive discovery of our own ignorance." - Will Durant
"One's first step in wisdom is to question everything - and one's last is to come to terms with everything." - Georg Christoph Lichtenberg
"There is no revenge so complete as forgiveness." - Josh Billings
"Kindness is more important than wisdom, and the recognition of this is the beginning of wisdom." -Theodore Rubin
Wednesday, December 5, 2012
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