1. An Experiment with Evolution – Developing an Eye Michael Guzman 21/2/2007

2. Outline Introduction and Background Project details Selected results Summary

3. Introduction and Background Genetic Algorithm Eye evolution – What we know by now Learn optics in 30 seconds

4. Genetic Algorithm Genetic algorithm is a probabilistic search algorithm. Iteratively transforms a population of individuals, each with an associated fitness value, into a new population of offspring objects. Darwinian principle of natural selection Applying operations which imitate nature’s genetic operations, such as crossover (sexual recombination) and mutation.

5. Genetic Algorithm

6. Eye evolution – What we know

7. Learn optics in 30 seconds

9. Project details Representation – The Genome Assumptions and Constants Fitness function

10. Representation – The Genome The purpose is to assume nothing The shape of the eye will we an ellipse – A-axis, B-axis The width of the opening to let light in Lens width Lens vertical location Lens focal length

11. Representation – The Genome A B Lens Y Lens Width Opening

12. Assumptions and Constants Mirror symmetry We start with very small B-axis almost a flat patch with the widest opening possible The starting focal length is very big – same as starting with no lens. Mutation probability 5% Mutation magnitude 5% Crossover probability 90%

13. Fitness function We consider the following factors 1.The smearing of a point on the retina 2.Area πAB 3.Perimeter – Ramanujan approximation 4.Illumination power - (2×L-radius)^2/focal^2 5.Resolution – different points projected on different photoreceptors. 6.Opening size – how much light goes in

14. Fitness function All factors normalized by their max-value The maximal values for the axes are 4 times bigger than the biggest eye existing today.

15. Selected results Why selected results?

16. Selected results – eye #1 0 500 2000 5000

17. Selected results – eye #2 0 1000 5000

18. Selected results – eye #3 Flat wide eye Minimal opening Lens adjacent to retina Very big focal length What went wrong?

19. Summary Using an unconditioned (almost) model of the eye, the results are nevertheless reasonable, and similar eyes can be found in nature. The project tries to simulate natural process from nature and therefore imposes some initial conditions on the individuals, a fact which prevents the genetic algorithm to show it full power. Some of the result are very improbable and they occur because of the method used to select the “parents” in each generation. It seems that otherwise than in size, no better eye than those we know from nature, has developed during the running of the algorithm.

20. Future work Finding a better general fitness function, giving more weight to : usage of the retina, ratio between axes etc… Trying special fitness function according to environmental conditions. Making a interactive web applet incorporating all of these.

21. References IBCV 2007 LectureNotes Evolutionary Computation and Artificial Life - BGU course LectureEvolutionary Computation and Artificial Life - BGU course Lecture Wikipedia A pessimistic estimate of the time required for an eye to evolve Nilsson & Pelger. Feynman lectures on physics Vol I ch.31 Field guide to Visual and Ophthalmic Optics bgu-lib QP.475.S385 Mathematics handbook by Korn&Korn McGRAW-HILL Various physics and analytical geometry books (russian)