2009-12-08
The Sydney Yahoo!7 office where I work is running a competition for the best Christmas-decorated workstation. Long before I joined two fellow technical Yahoos (Allan and Ben) had been collecting Golden Circle LOL soft drink cans, this continued until they had amassed over 400 of them! (I feel sorry for their wallets and pancreas.) Various construction projects with them have been attempted, but the Christmas competition naturally lead to a festive-themed construction.
I suggested construction using hexagons, partially because of my experience with hexagon numbered casing bundles for pyrotechnic purposes. Some quick maths was performed and it was determined that an 8th order stack could be assembled if we made the tower partially hollow. Cardboard hexagons were cut for each level to spread the load and stabilise the construction. While it would be possible to just stack the cans into the structure without the cardboard platters the result would have been far more fragile. We intended to use them even before it was determined we would need to make it partially hollow to achieve 8 tiers with the available cans (drinking the requisite amount for a completely solid tree today would have probably resulted in a hyperglycaemic coma for Allan and Ben).
The centred hexagon number for an n-th order hexagon is 3n^2 - 3n + 1, or 1, 7, 19, 37, 61, 91, 127, 169 for the orders 1-8. Solid construction would therefore have required 512 cans, but only 493 were available (including 65 V energy drink cans of identical geometry). I suggested tiling the outer layers with the green V cans for more tree-like effect, but it was decided to keep the structure as pure a "LOL-tree" as possible. In all 433 cans were used, only 8 of them V. The end result stands over 1 metre tall and consumes quite a significant amount of desk space.
Construction was filmed, Murali supplied a camera with time-lapse functionality and combined with my mini tripod we captured the process at 0.5 f/s.
The tree still needs a star. I may take in my Gooligum Christmas Star or build a custom one using some LEDs and an Atmel Tiny13. I happened to sketch the "K5" Charliplexing matrix and control vector table on the ferry this morning as part of an unrelated Christmas project. The software is yet to be written but the previous evening I threw together a 16-LED Christmas tree shaped arrangement as a test platform (although the K5 topology can drive 20 LEDs, 16 fits in 2 bytes per state vector as a simple initial try.) More on that project shortly.
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