Beautiful, Damn Hard, Increasingly Useful. That's Fractals.

Unfortunately, The World Has Not Been Designed For The Convenience Of Mathematicians.

Fractal Geometry Is Not Just A Chapter Of Mathematics, But One That Helps Everyman To See The Same World Differently.

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."

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.

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.