CDM
Some images illustrating concepts and examples in CDM.
Click to enlarge.
A reversible cellular automaton using Fredkin's construction.
A 6-state solution to the firing squad problem due to Mazoyer.
A binary width 7 cellular automaton that tests majority (with high probability).
The first 800 steps of the Marxen-Buntrock 5-state busy beaver machine.
Phasespace of elementary CA 150 on 9-bit configurations, cyclic
boundary conditions.
Phasespace of elementary CA 52 on 9-bit configurations, cyclic
boundary conditions.
A Sierpinski triangle generated by translating [3]^8 into coordinates via the
substitution 1 -> (0,0), 2 -> (0.5,1), 3 -> (1,0.2).
An optimal solution in the 5-disk Towers of Hanoi problem.
The classical bijection from N x N to N using a quadratic polynomial.
A bijection from N x N to N based on two quadratic polynomials.
Bitwise xor of all 6-bit numbers.
Up to 6 moves of a knight on an 8 by 8 chessboard.
An odd-parity cover for the 100 by 100 grid graph.
The involution f(x) = x + 1 acting on the Fibonacci rank of appearance of all
irrdeducible polynomial of degree 8 over GF(2).
The divisor lattice of 148176 and the Hasse diagram (as Boolean matrices).
The Hasse diagram of the divisor lattice of 148176 as a directed acyclic graph.
The von Neumann ordinal 5 in tree representation.
The von Neumann ordinal 5 in DAG representation with shared subexpressions.
A slightly nondeterministic finite state machine due to Moore that demonstrates
full exponential blow-up during deterministic simulation.
A slightly nondeterministic finite state machine based on a circulant graph
that demonstrates full exponential blow-up during deterministic simulation.
A highly nondeterministic finite state machine due to Jiraskova that demonstrates
full exponential blow-up during deterministic simulation.
The canonical DFA for the dihedral group D_4.
The canonical DFA for all even permutations over 4 letters.
Acceptance of all 180 minimal (6,1)-DFAs on words up to length 60.
The dihedral group D_6 acting on binary lists.
The alternating group A_6 acting on binary lists.
The stopping times for the first 2048 values of the Collatz function.
The up/down counts of the Collatz function for the first 100 powers of 3.
Lagrange interpolation of a few integral grid points.
A chaotic orbit of a transcendental point under a simple tent map.
500 steps of a 50-bit discrete version of the logistic function with parameter value 3.56.
The basin of attraction of 1 with respect to squaring modulo 32.
The relation associating squares and squares of successors modulo 512.
Redundancy of 10-digit hyper-binary representations.
Evolution of a one-dimensional sandpile.
The full transformation semigroup on three points.
Each transformation is iterated 5 times.
The Devil's Staircase:
a monotonic function no the unit interval such that f(0) = 0, f(1-x) = 1 - f(x)
and f(x/3) = f(x)/2.
A 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 ]]
The Farey sequence and Ford circles.
The first 250 points in the backward and forward orbit of 8 under Conway's T
function (log-lin plot).
The number of predecessors under the operation f(n) = n/2 using ceilings and floors.
A geometric proof of a summation identity involving binomials.
Enumerating Chomp configurations.
Iterating riffle shuffle.
Domino tilings equivalent under rotation and reflection.
4-colored necklaces of length 5.
A curve generated by a stack turtle.
A fractal rug generated by a stack turtle.
5 elastic particles bouncing between two fixed walls.
