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"seemingly non-random pattern arises" because for the Poisson examples above the expected value of the random variables in 5, while for the uniform distribution it is 25. Larger expected value makes numbers appear denser after the row normalization step, hence visually the graphs look different.

If one takes uniform distribution with the expected value 5, the picture would look similar to Poisson examples. E.g., for cases with 3 columns, graphs look like this.

For 20 columns, we start seeing rays for both distributions as can be seen here.

"seemingly non-random pattern arises" because for the Poisson examples above the expected value of the random variables is 5, while for the uniform distribution it is 25. Larger expected value makes numbers appear denser after the row normalization step, hence visually the graphs look different.

If one takes uniform distribution with the expected value 5, the picture would look similar to Poisson examples. E.g., for cases with 3 columns, graphs look like this.

For 20 columns, we start seeing rays for both distributions as can be seen here.

"seemingly non-random pattern arises" because for the Poisson examples, the expected value of the random variables in 5, while for the uniform it is 25. Larger expected value makes numbers appear denser after the row normalization step, hence visually the graphs look different.

If one takes uniform distribution with the expected value 5, the picture would look similar to Poisson examples. E.g., for cases with 3 columns, graphs look like this

"seemingly non-random pattern arises" because for the Poisson examples above the expected value of the random variables in 5, while for the uniform distribution it is 25. Larger expected value makes numbers appear denser after the row normalization step, hence visually the graphs look different.

If one takes uniform distribution with the expected value 5, the picture would look similar to Poisson examples. E.g., for cases with 3 columns, graphs look like this.

For 20 columns, we start seeing rays for both distributions as can be seen here.

"seemingly non-random pattern arises" because for the Poisson examples, the expected value of the random variables in 5, while for the uniform it is 25. If one takes uniform distribution with the expected value 5, the picture would look similar to Poisson examples. E.g., for cases with 3 columns, we have enter image description here

"seemingly non-random pattern arises" because for the Poisson examples, the expected value of the random variables in 5, while for the uniform it is 25. Larger expected value makes numbers appear denser after the row normalization step, hence visually the graphs look different.

If one takes uniform distribution with the expected value 5, the picture would look similar to Poisson examples. E.g., for cases with 3 columns, graphs look like this