(Page 0484) So what does one find if one allows templates that include nodes out to distance two? There are a total of 690 distinct non-trivial such templates -- and of ...

(Page 0499) Substitution systems that correspond to mobile automata can be thought of as having rules and initial conditions that are specially set up so that only one ...

(Page 0506) there will be an additional source of randomness: the arbitrariness of the path corresponding to the history that we have experienced. In many respects this ...

(Page 0554) starting with a single black cell and then applying a simple two-dimensional cellular automaton rule 250 times. But does the existence of this short description ...

(Page 0792) unprovability. But the issue remains why such phenomena have not been much more obvious in everyday work in mathematics. At some level I suspect the reason is ...

(Page 0803) this can be done for the fourth axiom system above. But if one removes just a single axiom from any of the axiom systems above then it turns out that they no ...

(Page 0843) But while traditional engineering has usually ended up finding ways to avoid searches for the limited kinds of systems it considers, the phenomenon of ...

(Page 0892f) Notes for: The World of Simple Programs | Substitution Systems Other examples [of substitution systems] (a) (Period-doubling sequence) After t steps, there are a ...

(Page 0904c) Notes for: Systems Based on Numbers | Elementary Arithmetic The 3 n+1 problem The system described here is similar to the so-called 3n+1 problem, in which one ...

(Page 0912c) Notes for: Systems Based on Numbers | Mathematical Constants Digit sequence properties Empirical evidence for the randomness of the digit sequences of Sqrt[n] , ...