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Let's say I have a grid of small cubes 20 x 20. I want to be able to make some amount of them 'grow' over one axis. The closest I had to this was use displacement with a cloud texture matched to an empty object that moves across the screen, but because it affects vertices instead of faces it doesn't look like cuboids anymore. Is there a way around this? enter image description here

(to further complicate things I'd like to be able to then assign different materials to sides so would be much better if starting point is cubes rather than plane)

zergkills
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I would keep the displace modifier but start from a single vertex that way it doesn't deform the meshes.

Start with a single vertex and add 2 Array modifiers

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Add a Displace modifier, setup a cloud texture, direction to Z, and set the coordinates to object, and add an Empty in the scene.

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Add 2 Screw modifiers along X and Y, set the steps to 1 and the angle to 0°

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Add a new vertex group to the object

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Add a Solidify modifier. Set the thickness to 0, the rim material to 1 and the output vertex group to the group you just created.

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Add a very large plane in your scene, set it to not render and set the viewport display to Bounds

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Add a Shrinkwrap modifier, target the large plane, set the wrap method to Project along Negative Z, and limit it only to the vertex group. I also added a Bevel modifier.

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Add 2 Materials, one for the Top & Bottom, and one for the Sides.

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Move the empty :

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Gorgious
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    That looks incredible! Would this allow to assign different materials to the faces? I.e. rather than just one material to the side and one to the top, with this method would I be able to assign a certain material to only say 3% of faces? thanks! appreciated – zergkills Mar 19 '21 at 14:10
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    Should be able to use Geometry -> Random Per Island to get random values for each – Allen Simpson Mar 19 '21 at 15:05
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    @zergkills Sure there are several options. Are you using Eevee or cycles for rendering ? – Gorgious Mar 19 '21 at 15:18
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    Problem: displace modifier has no visible effect. Solution: make sure the empty and the initial vertex are not in the same location (specifically, move the empty so that it is not the scaling factor of the cloud texture (default: .25 unit vectors) away from the vertex). – xgjxcxzk Mar 21 '21 at 01:23
  • thanks for your responses guys, I'm using Eevee currently but I can change if it helps – zergkills Mar 21 '21 at 23:28
  • hi all, thanks again for all your help with this. So far using the method of random per island I managed to get very close to where I need to be - https://imgur.com/a/KUDkWEt. This is using just constant colour ramp, but on assumption I'd like one of the materials to have different properties than just colour (like texturte over it for example), is there a way to do this? Thanks and sorry again for newbie questions – zergkills Mar 22 '21 at 10:45
  • This time it can warrant a new question on its own :) You can try plugging the random per island into a Math node set to greater than and then plug that into the fac input of a mix shader, then you can use 2 different shaders. Tweak the greater than value if you want just a certain percentage of one shader over the other. – Gorgious Mar 22 '21 at 11:13
  • That's incredible @Gorgious! Worked like a charm. But yeah, I think i will set this all up as a separate question – zergkills Mar 22 '21 at 11:31