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Assorted Pictures

Fredkin automaton

A reversible cellular automaton using Fredkin's construction.

Mazoyer's firing squad

A 6-state solution to the firing squad problem due to Mazoyer.

Marxen-Buntrock busy beaver

The first 800 steps of the Marxen-Buntrock 5-state busy beaver machine.

Computing majority on a cellular automaton

A binary width 7 cellular automaton that tests majority (with high probability).

A Sierpinski gasket

A Sierpinski triangle generated by translating [3]^8 into coordinates via the substitution 1 -> (0,0), 2 -> (0.5,1), 3 -> (1,0.2).

Towers of Hanoi

An optimal solution in the 5-disk Towers of Hanoi problem.

Log kernel

The 2-kernel of the binary digit count sequence.

Polynomial bijection

Cantor's classical bijection from N x N to N using a quadratic polynomial.

Another polynomial bijection

A bijection from N x N to N based on two quadratic polynomials.

Bitwise xor

Bitwise xor of all 6-bit numbers.

Knight moves

Up to 6 moves of a knight on an 8 by 8 chessboard.

Odd-parity cover

An odd-parity cover for the 100 by 100 grid graph.

Fibonacci rank of appearance

The involution f(x) = x + 1 acting on the Fibonacci rank of appearance of all irrededucible polynomial of degree 8 over GF(2).

Divisor lattice

The divisor lattice of 148176 and the Hasse diagram (as Boolean matrices).

Hasse diagram

The Hasse diagram of the divisor lattice of 148176 as a directed acyclic graph.

Von Neumann ordinal 5

The von Neumann ordinal 5 in tree representation.

Von Neumann ordinal 5

The von Neumann ordinal 5 in DAG representation with shared subexpressions.

Moore automaton

A slightly nondeterministic finite state machine due to Moore that demonstrates full exponential blow-up during deterministic simulation.

A circulant automaton

A slightly nondeterministic finite state machine based on a circulant graph that demonstrates full exponential blow-up during deterministic simulation.

A Jiraskova automaton

A highly nondeterministic finite state machine due to Jiraskova that demonstrates full exponential blow-up during deterministic simulation.

Canonical DFA for even 4-permutations

A DFA that recognizes all even permutations over a 4-letter alphabet.

Dihedral group action

The dihedral group D_6 acting on binary lists.

An alternating group action

The alternating group A_6 acting on binary lists.

Collatz stopping time

The stopping times for the first 2048 values of the Collatz function.

Collatz on powers of 3

The up/down counts of the Collatz function for the first 100 powers of 3.

A chaotic tent map

A chaotic orbit of a transcendental point under a simple tent map.

Discret logistic map

500 steps of a 50-bit discrete version of the logistic function with parameter value 3.56.

Successor squares mod 512

The relation associating squares and squares of successors modulo 512.

Knuth-Calkin

Redundancy of 10-digit hyper-binary representations.

One-dimensional sandpile

A few steps in the evolution of a one-dimensional sandpile.

The devil's staircase

A monotonic function on the unit interval such that f(0) = 0, f(1-x) = 1 - f(x) and f(x/3) = f(x)/2.

Wild surjection.

A rather bizarre surjection from the integers to the rationals: With[ {nn = Ceiling[Sqrt[n]]}, If[ n ≤ (nn-1)^2 + nn, nn/(n - (nn-1)^2), (nn^2 - n + 1)/nn ]]

Farey and Ford

The Farey sequence and Ford circles.

Conway's T function

The first 250 points in the backward and forward orbit of 8 under Conway's T function (log-lin plot).

Iterating the 1/2 operator

The number of predecessors under the operation f(n) = n/2 using ceilings and floors.

Riffle shuffle

A complete orbit under riffle shuffle.

Isomorphs

Domino tilings equivalent under rotation and reflection.

Necklaces

All 4-colored necklaces of length 5, in canonical order.

Stack turtle curve

A polygonal curve generated by a stack turtle.

Stack turtle rug

A fractal rug generated by a stack turtle.

by-nc-sa     © 2023 K. Sutner
Last modified: 2024/08/12