How I met the Biomorphs How I made Biomorphs
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Transcript of How I met the Biomorphs How I made Biomorphs
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
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2 greek words, which mean
«life» and «shape»
http://sprott.physics.wisc.edu/pickover/home.htm
1 – Definition and discovery of biomorphs
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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
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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
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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
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3 – My personal work :Home page
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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
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3 – My personal work :Picture for Season’s
Greetings
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3 – My personal w
ork :
Website
Biomorphsgallery
http://perso.club-internet.fr/lukem/biomorphe_aa.htm
To learn more
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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 ?