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Does anyone know how I can achieve this effect using illustrator? It's for a logo so I'd need to be able to create a version in black and white as well.
Draw some dots
Make a couple of different ones if you like, makes this look better
Colour them for the color version
Make art brushes. The black one needs to be colorization method: tints
Select all, Object > Transform, > Transform each and scale them randomly
Set the fill to black
Draw a red (or other unused color) filled circle
Select the lines and the red circle and Pathfinder panel: Outline
Select one of the red lines with direct selection tool and then Select > Same > Stroke color
Apply the art brush to the black lines and color their strokes whatever color you like.
For some of them you need to reverse direction of either the path or the brush.
Thanks for reaching out. I hope the suggestions shared by Monika helped resolve the problem.
Feel free to reach out if you have more questions or need assistance. We'd be happy to help.