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 2-kernel of the binary digit count sequence.

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.