1. The Dynamic Geometry of Geographical Vector Agents Yasser Hammam, Antoni Moore, Peter Whigham and Claire Freeman* Spatial Information Research Centre, Department of Information Science, *Department of Geography University of Otago, New Zealand

2. Overview Rationale The Vector Agent Model Implementation and Experimental Results Discussion Conclusions

3. Introduction Like Geographic Automata Systems, Vector Agents aim to introduce a bit of geographic realism to agent modelling But adds a systematic framework to the geometric element (“georeferencing convention”) With emphasis on irregular and dynamic aspects Aim to use boundary manipulation through simple controls to generate vector objects of a wide variety of shapes and complexities Pertinence to real world object characteristics are key to effectiveness

4. The Vector Agent Uses irregular fractal-like process to generate vector objects Also more direct boundary manipulation Aims To represent any discrete geographic phenomena through an irregular (or regular) data structure May move “bodily”, either based on a real world object, or is “born” with a non- deterministic shape boundary Abstracted so that it is able to define its own location in space

5. Regular – irregular Static – dynamic

6. Geometric manipulation Conventional midpoint displacement P new = 0.5 (P 1 + P 2 ) + µơ 0 2 -lh Where P 1 and P 2 are the start and end points of the line segment µ is a random number from a Gaussian ơ 0 is the S.D. of the Gaussian l is the level of recursivity h is the Hurst exponent governing roughness (= 2 – F.D.) Point displacement (not nec.midpoint) P new = (1 – r)P 1 + rP 2 + µơ 0 2 -lh Where r is proportion along line segment Edge / vertex displacement P = P + µơ 0

7. Sequence of growth bcdefa ghij

8. Results show evidence of both irregular and regular

9. Graphs

10. Shape control schematic SHAPE GROWTH RATE highlow Control of shape complexity high low MIDPOINT DISPLACEMENT VERTEX DISPLACEMENT EDGE DISPLACEMENT

11. Cities with similar shapes

12. Conclusion Vector agents are geometry-led agents Interplay of midpoint, edge and vertex displacement Evolved polygons have shape and complexity characteristics of real-world objects Able to be controlled by alteration of simple parameters

13. Conclusion Like GAS, each object has its own identity, an improvement on a group of contiguous CA cells But complexity and processing speed ramped up Next Test the system on a specific urban area Having tested on classical urban models 1 st Build in other elements of GAS States, transition rules, neighbourhood, neighbourhood rules