This is a research subproduct: the GIF below shows what happens if you consider a set of truncated gaussians (truncated so that they are zero outside a circle) with centers forming a tiling (the center locations are given by the vertices of a 5 by 5 ‘checkerboard’ plus the centers of the squares in the ‘checkerboard’) so that when added, they somehow overlap. The motion corresponds to what happens if you change the variance: if the variance is low, then the gaussians tend to be peaks, but if it is high, then there will be more overlap. Colors represent just the value of the sum of the truncated gaussian bumps, at each point of the square.
A gaussian Collapse
This is a research subproduct: the GIF below shows what happens if you consider a set of gaussians with centers forming a tiling (the center locations are given by the vertices of a 5 by 5 ‘checkerboard’ plus the centers of the squares in the ‘checkerboard’) so that when added, they somehow overlap. The motion corresponds to what happens if you change the variance: if the variance is low, then the gaussians tend to be peaks, but if it is high, then there will be more overlap. Colors represent just the value of the sum of the gaussian bumps, at each point of the square. This GIF ilustrates in (2D) a well known phenomenon in 1D. If you have the sum of two gaussian densities (essentially a mixture of gaussians) with same variance but with centers at different locations, there exists a critical value of the variance such that, below that value, the mixture will be bimodal, and above that value the mixture will have only one mode, located in the middle of the center of the constituting gaussians.
