Like many of us, [Tim]’I’ve seen videos online of circuit sculptures with illuminated LED filaments. But unlike most of us, he went one step further using graph theory to design glowing structures composed entirely of filaments.
The problem is not as simple as it seems at first glance: all segments must be illuminated, there must be as few powered nodes as possible, and to enable a single supply voltage, all paths between powered nodes must be the same length. Ideally, all filaments would carry the same amount of current, but even if that isn’t the case, the difference in brightness isn’t always noticeable. [Tim] found three ways to power these structures: direct current between fixed points, current supplied between alternating points to take different paths through the structure, and alternating current supplied between two fixed points (essentially a full-bridge incandescent rectifier).
To find workable structures, [Tim] circuits as directed graphs, where each intersection is a vertex and each filament a directed edge, and then develop filter criteria to find graphs corresponding to working circuits. In the case of power supply from fixed points, the problem turned out to be equivalent to the problem of geodesic coverage at the edges. Graphs that solve this problem are bipartite, providing an effective filtering criterion. The solutions found by this method often had uneven brightness. That’s why he also screened for circuits that can be broken down into a series of paths that visit each edge exactly once, so that each filament receives the same current. He also found some conditions to identify circuits using rectifier type AC drive, which you can see on the web page he created to visualize the different possible structures.
We’ve seen artistic illuminated circuit art before, some using LED filaments. This project doesn’t take exactly the same approach, but if you want to learn more about graph theory and route planning, read this article.
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