Mandelbrot Fractals: Hunting the Hidden Dimension  


It was in January OF 1944 that Benoit Mandelbrot fell in love with geometry, “in its most concrete and sensual form.”

”That part of geometry in which mathematics and the eye meet.”

During a math class, when Mandelbrot was nineteen years of age, at the Lycee du Parc in Lyon, young Benoit realized he could visualize algebra as geometric images. The class professor had been discussing a mathematical problem when Mandelbrot became instantly aware that he had the ability to change algebra into pictures. He then realized that once you can see pictures, the answer to a problem is obvious.

In 1958, Mandelbrot left France and joined IBM in America. It was here that Mandelbrot’s knowledge of visualizing problems was to prove very important.

Engineers at IBM had found an issue with transmitting computer information over telephone lines. Mandelbrot graphed the noise data, and noticed something that surprised him—no matter the time scale the graph looked similar, whether over one day, one hour, or one minute, or one second, the pattern remained constant. This reminded Mandelbrot of the Cantor Set, where a line is broken down into infinite recurring sets, and Helge von Koch’s “Snowflake,” where an iteration of a triangle creates an infinite length. Koch’s “Snowflake” is the earliest form of fractal.

Bringing these elements together, Mandelbrot developed a “theory of roughness” which he used to show that another dimension existed between 2-D and 3-D, this suggested there was a mathematical order to the seeming mess/chaos of the natural world. With the use of IBM computers, Mandelbrot proved his theory by producing a set of fractals in 1979.

Mandelbrot set images are made by sampling complex numbers and determining for each whether the result tends towards infinity when a particular mathematical operation is iterated on it. Treating the real and imaginary parts of each number as image coordinates, pixels are colored according to how rapidly the sequence diverges, if at all.  Did you get that?

Woody Allen Life Quotes

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Heywood “Woody” Allen (born Allan Stewart Konigsberg; December 1, 1935) is an American filmmaker, writer, actor, comedian, and musician whose career spans more than six decades.
He worked as a comedy writer in the 1950s, writing jokes and scripts for television and publishing several books of short humor pieces. In the early 1960s, Allen began performing as a stand-up comedian, emphasizing monologues rather than traditional jokes. As a comedian, he developed the persona of an insecure, intellectual, fretful nebbish, which he maintains is quite different from his real-life personality. In 2004, Comedy Central ranked Allen in fourth place on a list of the 100 greatest stand-up comedians, while a UK survey ranked Allen as the third greatest comedian.


When you are down, Monty Python raises your spirits!

From the Monty Python movie ‘Life of Brian.’

Some things in life are bad
They can really make you mad
Other things just make you swear and curse
When you’re chewing on life’s gristle
Don’t grumble, give a whistle
And this’ll help things turn out for the best

Always look on the bright side of life
Always look on the light side of life

If life seems jolly rotten
There’s something you’ve forgotten
And that’s to laugh and smile and dance and sing
When you’re feeling in the dumps
Don’t be silly chumps
Just purse your lips and whistle, that’s the thing

Always look on the bright side of life
(Come on)
Always look on the right side of life

For life is quite absurd
And death’s the final word
You must always face the curtain with a bow
Forget about your sin
Give the audience a grin
Enjoy it, it’s your last chance anyhow

So always look on the bright side of death
A just before you draw your terminal breath

Life’s a piece of shit
When you look at it
Life’s a laugh and death’s a joke, it’s true
You’ll see it’s all a show
Keep ’em laughin’ as you go
Just remember that the last laugh is on you

Always look on the bright side of life
Always look on the right side of life
(C’mon Brian, cheer up)
Always look on the bright side of life
Always look on the bright side of life

(Worse things happen at sea you know)

Always look on the bright side of life

I mean, what have you got to lose?
You know, you come from nothing
You’re going back to nothing
What have you lost? Nothing

Always look on the right side of life

Nothing will come from nothing, ya know what they say
Cheer up ya old bugga c’mon give us a grin (Always look on the right side of life)
There ya are, see
It’s the end of the film
Incidentally this record’s available in the foyer (Always look on the right side of life)

Some of us got to live as well, you know
(Always look on the right side of life)
Who do you think pays for all this rubbish
(Always look on the right side of life)
They’re not gonna make their money back, you know
I told them, I said to him, Bernie, I said they’ll never make their money back
(Always look on the right side of life)

Life: Quick, Intriguing, Random and quite Absurd

I don’t know where I’m going, but I’m on my way.
Carl Sandburg





Go to Heaven for the climate, Hell for the company.

Mark Twain




Happiness is having a large, loving, caring, close-knit family in another city.

George Burns
When we talk to God, we’re praying. When God talks to us, we’re schizophrenic.
Why do they call it rush hour when nothing moves?

Robin Williams
There are lots of people who mistake their imagination for their memory.
Josh Billings
The only true wisdom is in knowing you know nothing.



Life is full of misery, loneliness, and suffering – and it’s all over much too soon.

Woody Allen


Just cause you got the monkey off your back doesn’t mean the circus has left town.

George Carlin