Programming in Polygon R&D: Explorations with a Spatial Language II

  • Jim Morey
Original Paper


This paper introduces the language associated with a polygon microworld called PolygonR&D, which has the mathematical crispness of Logo and has the discreteness and simplicity of a Turing machine. In this microworld, polygons serve two purposes: as agents (similar to the turtles in Logo), and as data (landmarks in the plane). Programming the spatial behaviour of polygon agents is achieved by a simple variable-free language. Although limited in the number of instructions, the language allows for complex outcomes such as creation of sophisticated tilings, algorithm visualization, simulations, and even numerical computation. The ease of constructing the variety of examples shown in this paper indicates the microworld’s potential in both secondary and post-secondary education.


algorithm visualization decentralized microworld Logo tiling Turing machine 


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  1. Abbot E.A. (1884). Flatland: A Romance of Many Dimensions. Seeley & Co., Ltd., LondonGoogle Scholar
  2. Abelson H., diSessa A. (1981). Turtle geometry: the computer as a medium for exploring mathematics. MIT Press, Cambridge, MAGoogle Scholar
  3. Blikstein, P., Abrahamson, D. and Wilensky, U. (2005). Netlogo: Where we are, where we’re going. In I. Eisenberg and E. Eisenberg (Eds), Proceedings of the Fourth International Conference for Interaction Design and Children (IDC 2005), Boulder, ColoradoGoogle Scholar
  4. Dewdney A.K. (1989). Computer recreatation: Twodimensional Turing machines and turmites make tracks on a plane. Scientific American 261(3):124–127CrossRefGoogle Scholar
  5. Dijkstra E.W. (1972). Notes on structured programming. In: Dahl O.-J., Hoare C.A.R., Dijkstra E.W. (eds) Structured Programming. Academic Press, New York, pp. 1–82Google Scholar
  6. Gajardo A., Goles E. and Moreira A. (2001). Generalized Langton’s ant: Dynamical behavior and complexity. Lecture Notes in Computer Science 2010:259–270CrossRefGoogle Scholar
  7. Grünbaum B., Shephard G.C. (1989). Tilings and Patterns: An Introduction. W. H. Freeman and Company, New YorkGoogle Scholar
  8. Hopcroft J.E., Ullman J.D. (1979). Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading, MassGoogle Scholar
  9. Morey, J. (2005). TileLand.∼morey/CogEng/TileLand.html. last, last accessed: July 2005
  10. Morey, J. and Sedig, K. (2004). Using indexedsequential geometric glyphs to explore visual patterns. In Proceedings of Interactive Visualisation and Interaction Technologies (IV&IT 2004). AACEGoogle Scholar
  11. Papert S. (1980). Mindstorms: Children, Computers, and Powerful Ideas. Basic Books, New YorkGoogle Scholar
  12. Papert S. (1987). Computer Criticism vs. Technocentric Thinking. Educational Researcher 16(1):22–30CrossRefGoogle Scholar
  13. Penrose R. (1979). Pentaplexity. Mathematical Intelligencer 2:32–37Google Scholar
  14. Peterson I. (1988). The Mathematical Tourist: Snapshots of Modern Mathematics. W. H. Freeman and Company, New YorkGoogle Scholar
  15. Rader, C., Cherry, G., Brand, C., Repenning, A. and Lewis, C. (1998). Designing mixed textual and iconic programming languages for novice users. In Visual languages (Symposium on) (pp 187–194). IEEEGoogle Scholar
  16. Repenning, A. (1993). Agentsheets: A Tool for Building Domain-Oriented Dynamic, Visual Environments. PhD thesis, University of Colorado at BoulderGoogle Scholar
  17. Resnick M. (1996). Beyond the centralized mindset. Journal of Learning Sciences 5(1):1–22CrossRefGoogle Scholar
  18. Resnik M. (1994). Turtles, Termites and Traffic Jams – Explotations in Massively Parallel Mircoworlds. The MIT Press, Cambridge, MassachusettsGoogle Scholar
  19. Sedig, K., Morey, J. and Chu, B. (2002). Tileland: A microworld for creating mathematical art. In World Conference on Educational Multimedia and Hypermedia 2002 (pp. 1778–1783). AACEGoogle Scholar
  20. Senechal M. (1995). Quasicrystals and Geometry. Cambridge University Press, CambridgeGoogle Scholar
  21. Smith, D. C., Cypher, A. and Schmucker, K. (1996). Making programming easier for children. Interactions 3(5):58–67Google Scholar
  22. Travaglini, S. (2003). An Exploratory Study of Interactive Design Using a Tiling Microworld. Master’s thesis, University of Western OntarioGoogle Scholar
  23. Watt, S. (1998). Syntonicity and the psychology of programming. In J. Domingue and P. Mulholland (Eds), Proceedings of the Tenth Annual Meeting of the Psychology of Programming Interest Group (pp. 75–86)Google Scholar
  24. Weinstein, A. (2001). Groupoids: Unifying internal and external symmetry: A tour through some examples. In Ramsay, A. and Renault, J. (Eds), Groupoids in Analysis, Geometry, and Physics, Contemporary Mathematics (pp. 1–19). American Mathematical SocietyGoogle Scholar
  25. Wilensky, U. (2002). Netlogo. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.
  26. Wilensky U., Resnick M. (1999). Thinking in levels: A dynamic systems perspective to making sense of the world. Journal of Science Education and Technology 8(1):3–18CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceWesleyan CollegeMaconUSA

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