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# Symmetry, Branching, Modularity: Lego Tree

The tree experiment was designed to test out whether some characteristics of natural trees (branching, symmetry) could evolve as a consequence of the environment. The design of a tree in nature is a product of conflicting objectives: maximizing the exposure to light while keeping internal stability.

The experimental design for the tree has a narrow attachment base: Only three knobs. This provides very little sustentation for cantilevering, so the structure will have to be balanced to reach out. A light'' resource, coming from directions up, left and right, has one value per column or row. Light is absorbed'' by the first brick it touches -- and the fitness points given are equal to the distance from the absorption point to the x or y axis. The highest fitness would be a structure reaching out to completely cover the left, right and top borders (see fig. 2.29 and table 2.12).

There were no symmetry-oriented operators in our experiments, as could be, for example a reverse'' recombination operator that switched the orientation of a subpart. This means that symmetry is not encouraged by representational biases. Instead, the problem setup requires balancing the total weight of both sides. The tree did evolve, however, with a central symmetry with branches reaching out, by evolving the same type of solution separately on both sides.

The general layout of the evolved tree has several similarities with that of a real tree: there is a (somewhat twisted) trunk, with branches that become thinner as they reach out, and leaves'', bulky formations that maximize the surface at the end of the branch.

Table 2.12: Setup of the tree experiment.
 Bricks {1,2,4,6,8,10,12,16} Max Bricks 127 Base (0,-1)-(2,-1) x Range (-50,52) y Range (0,45) Fitness fL+fR+fT where S = structure

The tree is, among all our experiments, the one that most clearly illustrates the emergence of nested levels of organization, key indicator of what we call complex organization

• Level zero: individual bricks.
• Level 1: diagonal stacks and horizontal stacks of long bricks (on the branches), stacks of small bricks (at the tips),
• Level 2: trunk, U shaped branches, T structure at the top.
• Level 3: two tridents on top of each other, and a roof.
• Level 4: the entire structure.

Next: Recombination Example Up: Evolution of Adaptive Morphology Previous: Optimization
Pablo Funes
2001-05-08