File:Fixed points in Zhegalkin permutation 3.svg

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Summary

Description
Walsh matrix

The 16 fixed points in Zhegalkin permutation Ж3 (row 3 of Sloane's A197819), which has length 256   (compare File:Zhegalkin 256; fixed.svg)

Corresponding integers:   0, 30, 40, 54, 72, 86, 96, 126, 128, 158, 168, 182, 200, 214, 224, 254

The columns of the 8×16 matrix are the fixed points.
The rows are Walsh functions, which can also be found in the Walsh matrix shown on the right.
The 8×4 matrix on the left indicates which rows of the Walsh matrix they are.
Its upper half shows a Sierpiński triangle without the main diagonal, and the lower half shows the main diagonal.
(Hence the lower half of the 8×16 matrix is identical to the gray index matrix on top.)

ANF 30 to TT 30
TT 30 to ANF 30
illustrations of fixed point 30 in column 1
(algebraic normal form to truth table and back)
 
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Watchduck
You can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".
Other versions
256 fixed points in Ж4

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