Multidimensional Events in Multilevel Systems
Design involves assembling parts into whole to satisfy specified relationships. Binary relations between pairs of elements are not rich enough to represent the generality of this. Powerful though they are, graphs and networks must be extended to multidimensional networks to represent the many subtleties of complex systems. These structures underlie a natural theory of multilevel systems that has within it a kind of structural time defined by multidimensional events. Slow changing relational structure is discriminated from fast moving events captured by patterns of numbers. It will shown that the former acts as a kind of multilevel multidimensional backcloth for the multilevel multidimensional dynamic traffic of the latter. The theory will be illustrated by examples.
KeywordsBinary Relation Simplicial Complex Clock Time Multilevel System Shared Vertex
Unable to display preview. Download preview PDF.
- Atkin RH (1974) Mathematical Structure in human affairs. Heinemann, LondonGoogle Scholar
- Atkin RH (1981) Multidimensional Man. Penguin, LondonGoogle Scholar
- Barabasi A-L, (2003) Linked. Plume Books, Penguin, LondonGoogle Scholar
- Gould P, Johnson J, Chapman P (1984) The structure of television. Pion Books, LondonGoogle Scholar
- Johnson JH (1998) Relational structure in planning and design. Environment and Planning B, pp 57–67, Anniversary IssueGoogle Scholar
- Serras J (2005) ‘Extending TRANSIMS Technology to an Integrated Multilevel Representation. Computers in Urban Planning and Urban Management (CUPUM), CASA, University College London, UK, June 2005.Google Scholar