What do you mean by "memory"?  System memory, or video memory?  For video memory I know fairly certainly that, if the color depth and resolution is the same, then the video memory used will be the same.  For system memory I think it'll actually be a little bigger for the procedurally-generated bitmap, because a) you still need somewhere to stick that array of pixels and color depth before it is moved into video memory; and b) you need space to do the math to generate the bitmap in the first place.  Hard disk space, procedurally-generated textures are obviously going to be smaller, when dealing with large textures.

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