Transformers solve these using attention (for alignment), MLPs (for arithmetic), and autoregressive generation (for carry propagation). The question is how small the architecture can be while still implementing all three.
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By constraining our medium within a bounded region we can give ourselves a bit more flexibility on the appearance of fog within a scene. The simplest approach is to use primitives such as planes, spheres or boxes as bounding volumes. By determining the intersection of our view ray with these primitives we can find the length of the ray through the volume and calculate the total density using the same formula, once again assuming a constant density within the entire primitive.
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