2 Turing machines
A very practical Turing machine simulator is available at Turing Machine Simulator
Another one is avalaible at Online Turing Machine Simulator
A paper about Turing micros.
A funny speech about computability by Philip Wadler.
Proof for the Halting problem https://rjlipton.wordpress.com/2016/09/19/a-proof-of-the-halting-theorem/
4 Cellular automata
Other computation formalisms can be used than the ones we talk about this course. Cellular automata are one of them. What is truly amazing is to see that you can simulate a Turing machine using some cellular automaton. Here is an example :
5 P vs NP
5.1 Deolalikar Responds To Issues About His P≠NP Proof
Vinay Deolalikar claimed having found a proof that \(P \neq NP\). His proof is incomplete. However the discussion around the proof is very interesting.
6 Self-replicating programs or Quines :
List of Quines in many programming languages : http://www.nyx.net/~gthompso/quine.htm
The Tupper's formula is a formula that when plotted in 2D displays itself! Tupper's formula
A PDFTeX Quine: https://code.google.com/p/corkami/source/detail?r=1907