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Particle Tree Efficiency
So I have been given the project to design a poster where I need to create a “Career Tree”. The client wants the trees to look like this image.

She wants them to be similar but have variation in the direction of them. The end goal is a “forest” of these trees to be interconnected. What would be the easiest way to achieve this. If a particle system is needed in After Effects, how would I do that? My main concern is that I would not be able to stop the lines from overlapping.Thanks in advance,
Lucas