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The Beauty Of What I Happened By Extraordinary Chance To Put Together Is That Nobody Would Have Believed That This Is Possible, And Certainly I Didn't Expect That It Was Possible. I Just Moved From Step To Step To Step.

-Benoit Mandelbrot

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The Beauty Of What

Benoit Mandelbrot

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The Beauty Of What I Happened By Extraordinary Chance To Put Together Is That Nobody Would Have Believed That This Is Possible, And Certainly I Didn't Expect That It Was Possible. I Just Moved From Step To Step To Step.

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Everything Is Roughness, Except For The Circles. How Many Circles Are There In Nature? Very, Very Few. The Straight Lines. Very Shapes Are Very, Very Smooth. But Geometry Had Laid Them Aside Because They Were Too Complicated.

Clouds Are Not Spheres, Mountains Are Not Cones, Coastlines Are Not Circles, And Bark Is Not Smooth, Nor Does Lightning Travel In A Straight Line.

When People Ask Me What's My Field? I Say, On One Hand, A Fractalist. Perhaps The Only One, The Only Full-time One.

It Was A Very Big Gamble. I Lost My Job In France, I Received A Job In Which Was Extremely Uncertain, How Long Would Ibm Be Interested In Research, But The Gamble Was Taken And Very Shortly Afterwards, I Had This Extraordinary Fortune Of Stopping At Harvard To Do A Lecture And Learning About The Price Variation In Just The Right Way.

For Much Of My Life There Was No Place Where The Things I Wanted To Investigate Were Of Interest To Anyone.

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Pictures Were Completely Eliminated From Mathematics; In Particular When I Was Young This Happened In A Very Strong Fashion.

I Went To The Computer And Tried To Experiment. I Introduced A Very High Level Of Experiment In Very Pure Mathematics.

Humanity Has Known For A Long Time What Fractals Are. It Is A Very Strange Situation In Which An Idea Which Each Time I Look At All Documents Have Deeper And Deeper Roots, Never (how To Say It), Jelled.

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The Beauty Of What I Happened By Extraordinary Chance To Put Together Is That Nobody Would Have Believed That This Is Possible, And Certainly I Didn't Expect That It Was Possible. I Just Moved From Step To Step To Step.

I Spent Half My Life, Roughly Speaking, Doing The Study Of Nature In Many Aspects And Half Of My Life Studying Completely Artificial Shapes. And The Two Are Extraordinarily Close; In One Way Both Are Fractal.

One Of The High Points Of My Life Was When I Suddenly Realized That This Dream I Had In My Late Adolescence Of Combining Pure Mathematics, Very Pure Mathematics With Very Hard Things Which Had Been Long A Nuisance To Scientists And To Engineers, That This Combination Was Possible And I Put Together This New Geometry Of Nature, The Fractal Geometry Of Nature.

The Extraordinary Fact Is That The First Idea I Had Which Motivated Me, That Worked, Is Conjecture, A Mathematical Idea Which May Or May Not Be True. And That Idea Is Still Unproven. It Is The Foundation, What Started Me And What Everybody Failed To **** Prove Has So Far Defeated The Greatest Efforts By Experts To Be Proven.

Self-similarity Is A Dull Subject Because You Are Used To Very Familiar Shapes. But That Is Not The Case. Now Many Shapes Which Are Self-similar Again, The Same Seen From Close By And Far Away, And Which Are Far From Being Straight Or Plane Or Solid.

I Don't Seek Power And Do Not Run Around

I Didn't Feel Comfortable At First With Pure Mathematics, Or As A Professor Of Pure Mathematics. I Wanted To Do A Little Bit Of Everything And Explore The World.

Some Mathematicians Didn't Even Perceive Of The Possibility Of A Picture Being Helpful. To The Contrary, I Went Into An Orgy Of Looking At Pictures By The Hundreds; The Machines Became A Little Bit Better.

Everybody In Mathematics Had Given Up For 100 Years Or 200 Years The Idea That You Could From Pictures, From Looking At Pictures, Find New Ideas. That Was The Case Long Ago In The Middle Ages, In The Renaissance, In Later Periods, But Then Mathematicians Had Become Very Abstract.

Many Painters Had A Clear Idea Of What Fractals Are. Take A French Classic Painter Named Poussin. Now, He Painted Beautiful Landscapes, Completely Artificial Ones, Imaginary Landscapes. And How Did He Choose Them? Well, He Had The Balance Of Trees, Of Lawns, Of Houses In The Distance. He Had A Balance Of Small Objects, Big Objects, Big Trees In Front And His Balance Of Objects At Every Scale Is What Gives To Poussin A Special Feeling.

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I Conceived And Developed A New Geometry Of Nature And Implemented Its Use In A Number Of Diverse Fields. It Describes Many Of The Irregular And Fragmented Patterns Around Us, And Leads To Full-fledged Theories, By Identifying A Family Of Shapes I Call Fractals.

The Theory Of Chaos And Theory Of Fractals Are Separate, But Have Very Strong Intersections. That Is One Part Of Chaos Theory Is Geometrically Expressed By Fractal Shapes.

My Life Has Been Extremely Complicated. Not By Choice At The Beginning At All, But Later On, I Had Become Used To Complication And Went On Accepting Things That Other People Would Have Found Too Difficult To Accept.

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My Fate Has Been That What I Undertook Was Fully Understood Only After The Fact.

In Mathematics And Science Definition Are Simple, But Bare-bones. Until You Get To A Problem Which You Understand It Takes Hundreds And Hundreds Of Pages And Years And Years Of Learning.

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Nobody Will Deny That There Is At Least Some Roughness Everywhere

Think Not Of What You See, But What It Took To Produce What You See.

I Spent My Time Very Nicely In Many Ways, But Not Fully Satisfactory. Then I Became Professor In France, But Realized That I Was Not - For The Job That I Should Spend My Life In.

I've Been A Professor Of Mathematics At Harvard And At Yale. At Yale For A Long Time. But I'm Not A Mathematician Only. I'm A Professor Of Physics, Of Economics, A Long List. Each Element Of This List Is Normal. The Combination Of These Elements Is Very Rare At Best.

I Conceived, Developed And Applied In Many Areas A New Geometry Of Nature, Which Finds Order In Chaotic Shapes And Processes. It Grew Without A Name Until 1975, When I Coined A New Word To Denote It, Fractal Geometry, From The Latin Word For Irregular And Broken Up, Fractus. Today You Might Say That, Until Fractal Geometry Became Organized, My Life Had Followed A Fractal Orbit.

There Are Very Complex Shapes Which Would Be The Same From Close By And Far Away.

For Most Of My Life, One Of The Persons Most Baffled By My Own Work Was Myself.

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A Formula Can Be Very Simple, And Create A Universe Of Bottomless Complexity.

There Is A Saying That Every Nice Piece Of Work Needs The Right Person In The Right Place At The Right Time.

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Both Chaos Theory And Fractal Have Had Contacts In The Past When They Are Both Impossible To Develop And In A Certain Sense Not Ready To Be Developed.

I Didn't Want To Become A Pure Mathematician, As A Matter Of Fact, My Uncle Was One, So I Knew What The Pure Mathematician Was And I Did Not Want To Be A Pure - I Wanted To Do Something Different.

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Being A Language, Mathematics May Be Used Not Only To Inform But Also, Among Other Things, To Seduce.

The Mandelbrot Set Is The Most Complex Mathematical Object Known To Mankind.

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Order Doesn't Come By Itself.

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Round About The Accredited And Orderly Facts Of Every Science There Ever Floats A Sort Of Dustcloud Of Exceptional Observations, Of Occurrences Minute And Irregular And Seldom Met With, Which It Always Proves More Easy To Ignore Than To Attend To.

If You Assume Continuity, You Can Open The Well-stocked Mathematical Toolkit Of Continuous Functions And Differential Equations, The Saws And Hammers Of Engineering And Physics For The Past Two Centuries (and The Foreseeable Future).

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A Fractal Is A Mathematical Set Or Concrete Object That Is Irregular Or Fragmented At All Scales...

If You Have A Hammer, Use It Everywhere You Can, But I Do Not Claim That Everything Is Fractal.

I Was Asking Questions Which Nobody Else Had Asked Before, Because Nobody Else Had Actually Looked At Certain Structures. Therefore, As I Will Tell, The Advent Of The Computer, Not As A Computer But As A Drawing Machine, Was For Me A Major Event In My Life. That's Why I Was Motivated To Participate In The Birth Of Computer Graphics, Because For Me Computer Graphics Was A Way Of Extending My Hand, Extending It And Being Able To Draw Things Which My Hand By Itself, And The Hands Of Nobody Else Before, Would Not Have Been Able To Represent.

Asking Questions

A Fractal Is A Way Of Seeing Infinity.

When The Weather Changes And Hurricanes Hit, Nobody Believes That The Laws Of Physics Have Changed. Similarly, I Don't Believe That When The Stock Market Goes Into Terrible Gyrations Its Rules Have Changed. It's The Same Stock Market With The Same Mechanisms And The Same People.

I Claim That Many Patterns Of Nature Are So Irregular And Fragmented, That, Compared With Euclid - A Term Used In This Work To Denote All Of Standard Geometry - Nature Exhibits Not Simply A Higher Degree But An Altogether Different Level Of Complexity ... The Existence Of These Patterns Challenges Us To Study These Forms That Euclid Leaves Aside As Being "formless," To Investigate The Morphology Of The "amorphous."

The Straight Line Has A Property Of Self-similarity. Each Piece Of The Straight Line Is The Same As The Whole Line When Used To A Big Or Small Extent.

If You Look At A Shape Like A Straight Line, What's Remarkable Is That If You Look At A Straight Line From Close By, From Far Away, It Is The Same; It Is A Straight Line.

I Had Very, Very Little Training In Taking An Exam To Determine A Scientist's Life In France.

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