In N-dimensional simplex noise, the squared kernel summation radius $r^2$ is $\frac 1 2$ for all values of N. This is because the edge length of the N-simplex $s = \sqrt {\frac {N} {N + 1}}$ divides out of the N-simplex height $h = s \sqrt {\frac {N + 1} {2N}}$. The kerel summation radius $r$ is equal to the N-simplex height $h$.

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