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## The Long Bridge: Cantilevering

The Long Bridge'' experiment used an straightforward setup: A base'' of up to 40 knobs and a distant target point'' at (-300,0) (table 2.10).

Table 2.10: Long bridge problem specification (x,y Lego units = 8mm 9.6 mm.)
 Bricks {4,6,8,10,12,16} Max Bricks 127 Base (0,-1)-(-39,-1) x Range (-310,41) y Range (-2, 80) Initial Brick 6-brick at (0,0) Target Point T (-300,0) Fitness(S)

We left the experiment run for a long time, until it ceased producing further improvements. The idea was to see how long a beam structure we could design. The resulting structure was larger than we had imagined was possible (figs. 2.20 and 2.21).

The general principle discovered by this structure is that of cantilevering. A cantilevered beam is a well known architectural design problem, solved here by founding a thin, long, light beam on a strong base; counter-balancing it reduces stress (fig. 2.22).

Several hierarchical levels of organization are present in this structure:

• Level zero: Individual bricks.
• Level 1: Useful brick arrangements. Four-brick boxes'' (fig. 2.23) are an example.
• Level 2: Diagonal columns (the base is made up of layered columns).
• Level 3: Functional parts: base, beam, cantilever.
• Level 4: The entire structure.

Level 1 of complexity is interesting. Due to the widespread use of recombination, subsolutions such as the brick box'' are evolutionarily stable. They are used throughout the structure, be it beam, base or counterbalance, and give the structure a modular quality.

A random recombination has a higher chance of surviving if the bricks replaced are laid out in a similar pattern, thus evolutionary runs such as this one will favor recombinable structures.

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Pablo Funes
2001-05-08