{"id":966,"date":"2012-02-11T19:19:16","date_gmt":"2012-02-12T00:19:16","guid":{"rendered":"https:\/\/ideasillustrated.com\/blog\/?p=966"},"modified":"2020-11-12T14:27:24","modified_gmt":"2020-11-12T14:27:24","slug":"thick-as-a-lego-brick","status":"publish","type":"post","link":"https:\/\/ideasillustrated.com\/blog\/2012\/02\/11\/thick-as-a-lego-brick\/","title":{"rendered":"Thick as a [LEGO] Brick"},"content":{"rendered":"

A few weeks ago,\u00a0Samuel Arbesman\u00a0wrote an article<\/a> in Wired touching on the mathematical properties\u00a0inherent in LEGO structures. In it, he discussed the results of a 10-year old study<\/a> of natural and human-made networks that described how the number of distinct components in a network increased with the overall size of the network.<\/p>\n

The study showed\u00a0that the LEGO systems did indeed follow this rule. However,\u00a0Arbesman noted that the relationship increased sublinearly, suggesting that LEGO systems were under some form of selection\u00a0pressure (like the economics of production)\u00a0that made\u00a0it more expensive to grow the system and create new types of pieces. He was curious to see whether or not these findings would hold true with a more complete list of LEGO sets available today (n=389 in the 2002 study).<\/p>\n

After using a webcrawler to pull the data<\/a> for the available sets and their component pieces, I was presented with a list of\u00a0over 6,800 individual toys or kits. Not all of these kits fit the criteria of the original study, which investigated sets that were designed to build somthing specific as opposed to generic collections of pieces.<\/p>\n

Paring down this list turned out to be the most difficult part of this excercise. I ended up eliminating any set had words like “accessories,” “supplemental,”\u00a0 or “universal building set” in the name. I also removed entire toy lines such as DUPLO<\/a>, Clikits, and Primo\/Baby<\/a>\u00a0which didn’t seem to fit in the standard LEGO system. Basically, I tried to include anything with a brick, plate, or tile that had a picture of a single object on the box. I ended up with about 3,750 sets … or about ten times the number in the original study.<\/p>\n

So, do the results hold up with the new data? At first glance, it appears they do. Both the log-log and semi-log plots described in the study are reproduced here with the larger counts. Note that a power-law relationship still\u00a0appears to fit the data better than a logarithmic relationship.<\/p>\n

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Once I had access to all of that cool LEGO data, of course, I couldn’t resist a few more visuals. The first thing I developed was an interactive chart that lets you navigate the size and complexity data to see specific kits. Check out the links for pictures and parts lists.<\/p>\n