Plünnecke Graph Builder

Experiment with growth ratios |kA − ℓA| / |A| in ℤ/pℤ. Fix one of k, ℓ and visualize the function of the other.

Prime p

Tip: Small growth often appears when A is an arithmetic progression (interval) mod p.

|A|

Current ratio

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Fixed

k=2

Free range

ℓ = 0…8

Sweep mode

Fixed value (nonnegative integer)

Max free value (inclusive)

0A is taken to be {0}. For k,ℓ ≥ 1 we iteratively form k-fold sums and ℓ-fold sums, then the difference set kA − ℓA = {x − y}. Ratio is |kA − ℓA| / |A|.

Set A (inner ring)

Points in kA − ℓA are visualized numerically in the plot.