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).

  

Figure 2.20: Long Bridge.

 

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).

  

Figure 2.21: Long Bridge Scheme. The network represents the distribution of loads as assigned by our simulator; thicker lines correspond to stronger links several knobs wide. Light links are stressed to the limits, whereas dark ones are cool.

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).

  

Figure 2.22: Long bridge organization: base (dark grey), cantilevered beam (white) and counterbalance (light grey).

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.
  
    

  Figure 2.23: Four bricks in a ``box'' arrangement. This composite building block is used many times for the solution to the long bridge problem.

  

  
  

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.