How I met the BiomorphsHow I made Biomorphs

Jean-LouisSeichepine

TP LE03 – 17th December 2004

2 How I met the BiomorphsHow I made Biomorphs

1 – Definition and discovery of biomorphs

2 – My meeting with them

3 – My personal work

4 – Future projects

3 How I met the BiomorphsHow I made Biomorphs

2 greek words, which mean

«life» and «shape»

http://sprott.physics.wisc.edu/pickover/home.htm

1 – Definition and discovery of biomorphs

4 How I met the BiomorphsHow I made Biomorphs

1989

An article in« Pour la science »

(« For the science ») N°143 (septembre 1989)

French version of « Scientific American »

« Partie de pêche »(« Fishing party »)

pp. 98 à 101 N°143

2 – My meeting with them

Some biomorphs viewed through a microscope, together with the function where they come from

5 How I met the BiomorphsHow I made Biomorphs

Biomorphs live in the imaginary plan, where each point M0 is associated to a complex number

z0 = a0 + i b0

a0 , b0 : real numbersi : square root of -1

A biomorph is generated by a function f of a complex number giving another complex number, like :

f(z) = zA + B + C i + D cos(z) + E sin(z) + F ez + G zz

A, B, C, D, E, F, G : chosen real numbersFor each z0 in the considered area :

z1 = f(z0), z2 = f(z1), ……. , z10 = f(z9)At each step :

zn = an + i bn rn = I zn I

If rn > 10, calculations are stopped If it does not happen calculations are stopped after 10 iterations

h(M0) = min ( I an I, I bn I )The biomorph is then obtained as a map of h

2 – My meeting with them

Theory

6 How I met the BiomorphsHow I made Biomorphs

1997

Playing with my own

computer

2 – My meeting with them

7 How I met the BiomorphsHow I made Biomorphs

3 – My personal work :Wallpaper

8 How I met the BiomorphsHow I made Biomorphs

3 – My personal work :Home page

9 How I met the BiomorphsHow I made Biomorphs

Brain storming

4 – It is recommended

to steal the ideas of others

3 – The number of ideas is more

important than their quality

2 – The free imagination is

requested

1 – Any reproach is forbidden

Rules for a maximum efficiency

3 – My personal work :Illustation for a presentation

10 How I met the BiomorphsHow I made Biomorphs

3 – My personal work :Picture for Season’s

Greetings

11 How I met the BiomorphsHow I made Biomorphs

3 – My personal w

ork :

Website

Biomorphsgallery

http://perso.club-internet.fr/lukem/biomorphe_aa.htm

To learn more

12 How I met the BiomorphsHow I made Biomorphs

4 – Future

projects

But immediatly :

Thank you for your attention, At your disposal for questions, And have a nice end of the year !

Questions for the future :

Is that science or art ?

What are the relationships between mathematics and beauty ?

If I proposed a February activity on biomorphs, who would be interested ?