Mathieu Ledru
January 21, 2007
47

# Fractals

January 21, 2007

## Transcript

6. ### The fractals in the human’s body This cauliflower is fractal!

Some elements of the body’s corp are the same! Let us prove it @matyo91 30-01-2007
7. ### The lungs Without that structure, the lungs would took 2.8m3

@matyo91 30-01-2007
8. ### All the objects we view have the same property A

fragment of the object look as the object itself! This is call : Self-similarity Self-similarity @matyo91 @matyo91 30-01-2007

13. ### Menger sponge The number of cubes increases by : 20^n.

Where n is the number of iterations performed on the first cube @matyo91 30-01-2007
14. ### How do we name these shapes with this self-similarity principe?

@matyo91 30-01-2007

« fractal »
16. ### It has a fine structure at arbitrarily small scales It

possess the self-similarity structure It can have a non-integer dimension property of a fractal’s object @matyo91 @matyo91 30-01-2007
17. ### The fractal’s dimension @matyo91 30-01-2007 Yes, certain objects are of

non-integer dimension
18. ### That is to say 1 the side of the initial

triangle. Then in the second stage, the side of the three triangles and we got a shape twice larger. d= log(3)/ log(2) = 1.58   For S(3), we got   d = log(27)/log(8) = 1.58 Dimension of the Sierpinsky’s triangle @matyo91 30-01-2007
19. ### Beauty @matyo91 30-01-2007 About the beautiful images fractals generated by

transformations.

21. ### Process @matyo91 30-01-2007 z0=0   z n+1 = zn2 +

c and c is a complex. For each pixel of the screen, we associate a value of c.   If zi has a module higher than 2, the sequence diverges and the pixel is drawn color i.   When the sequence does not diverge, the pixel in black is colored
22. ### Particularity @matyo91 30-01-2007 We always find the original size when

we zoom in!!!

24. ### The virtual images @matyo91 30-01-2007 On the computer, one can

reveal virtual images of natural objects of a great complexity and of one extraordinary resemblance.
25. ### In industry @matyo91 30-01-2007 They are in the origin of

: new materials of insulation like polymers. Processes of recovery of oil by injection of fluids under pressure in the porous rocks Etc.

27. ### Hello! I Am Mathieu Ledru You can contact me at

@matyo91 @matyo91 Thanks! Any questions? 30-01-2007