I am trying to replicate this particle effect in blender - https://vimeo.com/219576444 I especially want the particles to change their direction 90 degrees, like in the video.
Particularly this part
How can I do this in a blender?
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I would suggest a slightly different approach. And I suspect this is what he did the more I look at it.
If you want to get fancier, you can animate the turns procedurally on the object so it randomizes the turns. Additionally, the object you are animating can be a particle system to get more control over the trails that you might want.
This is based partially on the suggestions of Richard Marklew on Blender artists. https://blenderartists.org/t/offset-particle-object-animation/489919/3