(Page 0780) any proof -- regardless of length -- exists for a specific result in a mathematical system with particular axioms. So what are the implications of this? Probably ...

(Page 0645) [No text on this page] Captions on this page: The universal cellular automaton emulating elementary rule 254. Each cell in rule 254 is represented by a block of ...

(Page 0649) [No text on this page] Captions on this page: Details of how the universal cellular automaton emulates rule 254. Each of the blocks in the universal cellular ...

(Page 1080e) Notes for: Processes of Perception and Analysis | Auditory Perception [Sounds based on] musical scores Instead of taking a sequence to correspond directly to the ...

(Page 0783) Yet if a system is computationally irreducible this will inevitably not be possible. For at any point the system will always in effect be able to do more things ...

(Page 1011b) Notes for: Implications for Everyday Systems | Growth of Plants and Animals Tumors In both plants and animals tumors seem to grow mainly by fairly random ...

(Page 0150) [No text on this page] Captions on this page: Examples of iterated maps starting from simple initial conditions. At each step there is a number x between 0 and 1 ...

(Page 0355) inevitable -- as discussed on page 255 and illustrated above -- that the behavior of the system will eventually repeat. In some cases the basic structure of a ...

(Page 0868a) Notes for: The Crucial Experiment | How Do Simple Programs Behave? Special-purpose hardware [for cellular automata] The simple structure of cellular automata ...

(Page 0427) The pictures on the facing page show typical examples of pigmentation patterns in animals, and demonstrate that even across a vast range of different types of ...