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Is there a way to generate a grid of points as a texture? Something like this (without the box): enter image description here

And/or is there a way to create my own texture node with Python? If there's API for that I guess I can also write my own procedure texture.

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A wave texture will give you a gradient from black to white. Two of them rotated ninety degrees from each other gives you a grid. A colour ramp can then adjust the size of each square, which with the gradient becomes circular at smaller sizes.

Set the colour ramp to use constant interpolation to get a sharper edge. Adjust the position of the ramp stops to adjust the size of the spots. The mapping nodes and scale of the wave texture will adjust the overall placement.

sample dots texture

node setup

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