Overlapping wires?

The schematic is only an abstraction of the layout. Whilst you probably want to pack your LEDs together in the PCB layout, you can space them out and rearrange in a clear, separate and logical order on the schematic. If you try and connect it up as you have laid them out it will be totally unreadable and impossible to follow any connections with any certainty and you are very likely to make a mistake.

I would suggest that you might find that this sort of layout might be handled in a couple of different ways - it might well be a good design to use a hierarchical schematic for. Alternatively, I would think that this sort of layout would be better described using a series of busses.This FAQ might give you some pointers Hierarchical or flat schematic design, what is best for me? (How to deal with multi page schematics?)

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