Treasure Hunting in Virtual Environments: Scaling Laws of Human Motions and Mathematical Models of Human Actions in Uncertainty

  • Dimitri Volchenkov
  • Jonathan Helbach
  • Marko Tscherepanow
  • Sina Kühnel
Part of the Nonlinear Systems and Complexity book series (NSCH, volume 8)


Searching experiments conducted in different virtual environments over a gender balanced group of people revealed a gender irrelevant scale-free spread of searching activity on large spatiotemporal scales. The better performance of men in virtual environments can be associated with the regularly renewed computer game experience, essentially in games played through a first-person perspective. We suggested a simple self-organized critical model of search, in which the experimentally observed scale-free behavior can be interpreted as a trade-off between the value of exploitation versus exploration amid uncertainty.


Virtual Environment Root Mean Square Fluctuation Computer Game Experience Spatial Graph Quadratic Hyperbola 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The treasure hunting experiments have been supported by the Cognitive Interaction Technology—Center of Excellence (CITEC, Bielefeld University).

D.V. gratefully acknowledges the financial support by the project MatheMACS (“Mathematics of Multilevel Anticipatory Complex Systems”), grant agreement no. 318723, funded by the EC Seventh Framework Programme FP7-ICT-2011-8.


  1. 1.
    Atkinson RPD, Rhodes CJ, MacDonald DW, Anderson RM (2002) Scale-free dynamics in the movement patterns of jackals. Oikos 98(1):134–140CrossRefGoogle Scholar
  2. 2.
    Bak P, Tang C, Wiesenfeld K (1987) Self-organized criticality: an explanation of 1∕f noise. Phys Rev Lett 59(4):381–384MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bartumeus F (2007) Lévy processes in animal movement: an evolutionary hypothesis. Fractals 15(2):151–162CrossRefGoogle Scholar
  4. 4.
    Bartumeus F, Catalan J, Viswanathan GM, Raposo E, da Luz MGE (2008) The influence of turning angles on the success of non-oriented animal searches. J Theor Biol 252:43–55CrossRefGoogle Scholar
  5. 5.
    Bartumeus F, Levin SA (2008) Fractal reorientation clocks: Linking animal behavior to statistical patterns of search. PNAS 105(49):19072–19077. doi:10.1073/pnas.0801926105CrossRefGoogle Scholar
  6. 6.
    Bartumeus F (2009) Behavioral intermittence, levy patterns, and randomness in animal movement. Oikos 118:488–494Google Scholar
  7. 7.
    Blanchard Ph, Volchenkov D (2008) Intelligibility and first passage times in complex urban networks. Proc Roy Soc A 464:2153–2167. doi:10.1098/rspa.2007.0329MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Blanchard Ph, Volchenkov D (2009) Mathematical analysis of urban spatial networks. Springer Series: Understanding complex systems. Springer, Berlin/HeidelbergzbMATHGoogle Scholar
  9. 9.
    Blanchard Ph, Volchenkov D (2011) Introduction to random walks on graphs and databases. Springer Series: Synergetics. Springer, Berlin/HeidelbergCrossRefGoogle Scholar
  10. 10.
    Brockmann D, Hufnagel L, Geisel T (2006) The scaling laws of human travel. Nature 439:462–465CrossRefGoogle Scholar
  11. 11.
    Buldyrev SV, Havlin S, Kazakov AYa, da Luz MGE, Raposo EP, Stanley HE, Viswanathan GM (2001) Average time spent by Lévy flights and walks on an interval with absorbing boundaries. Phys Rev E 64:041108Google Scholar
  12. 12.
    Cohen JD, Aston-Jones G (2005) Cognitive neuroscience: decision amid uncertainty. Nature 436:471–472CrossRefGoogle Scholar
  13. 13.
    Cohen JD, McClure SM, Yu AJ (2007) Should I stay or should I go? How the human brain manages the trade-off between exploitation and exploration. Phil Trans R Soc Lond B 362:933–942CrossRefGoogle Scholar
  14. 14.
    Colzato LS, van Leeuwen PJA, van den Wildenberg WPM, Hommel B (2010) DOOM’d to switch: superior cognitive flexibility in players of first person shooter games. Front Psychol 1:8Google Scholar
  15. 15.
    Cutmore TRH, Hine TJ, Maberly KJ, Langford NM, Hawgood G (2000) Cognitive and gender factors influencing navigation in a virtual environment. Int J Hum Comput Stud 53:223–249CrossRefGoogle Scholar
  16. 16.
    Darken RP, Sibert JL (1993) A toolset for navigation invirtual environments. Proceedings of ACM User Interface Software and Technology, Atlanta, GA, pp 157–165, 3–5 November 1993Google Scholar
  17. 17.
    Devlin AS, Bernstein J (1995) Interactive wayfinding: Use of cues by men and women. J Environ Psychol 15:23–38CrossRefGoogle Scholar
  18. 18.
    Dillon BA (2009) Event wrap-up: Girls “N” Games 2006. Gamasutra. 18 May 2006Google Scholar
  19. 19.
    Federal Highway Administration (1997) Nationwide personal transportation study 1995: Transportation user’s views of quality. U.S. Department of Transportation, Washington, DCGoogle Scholar
  20. 20.
    Flajolet P, Sedgewick R (2009) Analytic combinatorics. Cambridge University Press, New YorkCrossRefzbMATHGoogle Scholar
  21. 21.
    Gittins JC (1989) Multi-armed bandit allocation indices. Wiley - Interscience Series in Systems and Optimization. Wiley, ChichesterzbMATHGoogle Scholar
  22. 22.
    Hamilton E (2009) The girl gamer’s manifesto. GameSpot. 11 February 2009Google Scholar
  23. 23.
    Hurst HE, Black RP, Simaika YM (1965) Long-term storage: an experimental study. Constable, LondonGoogle Scholar
  24. 24.
    Klatzky RL, Loomis JM, Beall AC, Chance SS, Golledge RG (1998) Spatial updating of self-position and orientation during real, imagined, and virtual locomotion. Psychol Sci 9(4): 293–298CrossRefGoogle Scholar
  25. 25.
    Komin N, Erdmann U, Schimansky-Geier L (2004) Random walk theory applied to daphnia motion. Fluctuation Noise Lett 4:L151–L159CrossRefGoogle Scholar
  26. 26.
    Lawton CA (1994) Gender differences in way-finding strategies: Relationship to spatial ability and spatial anxiety. Sex Roles 30(11–12):765–779CrossRefGoogle Scholar
  27. 27.
    Levandowsky M, Klafter J, White BS (1988) Swimming behavior and chemosensory responses in the protistan microzooplankton as a function of the hydrodynamic regime. Bull Mar Sci 43:758–763Google Scholar
  28. 28.
    Levy M, Solomon S (1996) Power Laws are Logarithmic Boltzmann Laws. Int J Mod Phys C 7(4):595–601CrossRefGoogle Scholar
  29. 29.
    Moffat SD, Hampson E, Hatzipantelis M (1998) Navigation in a “virtual” maze: sex differences and correlation with psychometric measures of spatial ability in humans. Evol Hum Behav 19:73–78CrossRefGoogle Scholar
  30. 30.
    Nathan R, Getz WM, Revilla E, Holyoak M, Kadmon R, Saltz D, Smouse PE (2008) A movement ecology paradigm for unifying organismal movement research. PNAS 105(49): 19052–19059CrossRefGoogle Scholar
  31. 31.
    Riecke BE, Schulte-Pelkum J, Bülthoff HH (2005) Perceiving simulated ego-motions in virtual reality—comparing large screen displays with HMDs. SPIE 2005 Conference Proceedings, San Jose, USA, 2005Google Scholar
  32. 32.
    Schimansky-Geier L, Erdmann U, Komin N (2005) Advantages of hopping on a zigzag course. Phys A 351(1):51–59CrossRefGoogle Scholar
  33. 33.
    Shlesinger M, Zaslavsky GM, Klafter J (1993) Strange kinetics. Nature 363:31–37CrossRefGoogle Scholar
  34. 34.
    Sims DW et al (2008) Scaling laws of marine predator search behaviour. Nature 451: 1098–1102CrossRefGoogle Scholar
  35. 35.
    Two AVI video fragments showing the records of actual searching experiments from the first-person perspective can be found at (the VE model A) and (the VE model B)
  36. 36.
    Viswanathan GM, Afanasyev V, Buldyrev SV, Murphy EJ, Prince PA, Stanley HE (1996) Lévy flight search patterns of wandering albatrosses. Nature (London) 381:413CrossRefGoogle Scholar
  37. 37.
    Viswanathan GM, Buldyrev S, Havlin S, da Luz MGE, Raposo EP, Stanley HE (1999) Optimizing the success of random searches. Nature (London) 401:911CrossRefGoogle Scholar
  38. 38.
    Viswanathan GM, Raposo EP, da Luz MGE, Lévy flights and uperdiffusion in the context of biological encounters and random searches. Phys Life Rev 5(3):133–150Google Scholar
  39. 39.
    Voyer D, Voyer S, Bryden MP (1995) Magnitude of sex differences in spatial abilities: a meta-analysis and consideration of critical variables. Psychol Bull 117:250–270CrossRefGoogle Scholar
  40. 40.
    Wann JP, Mon-Williams M (1996) What does virtual reality NEED? Human factors issues in the design of three-dimensional computer environments. Int J Hum Comput Stud 44:829–847CrossRefGoogle Scholar
  41. 41.
    Werner S, Long P (2003) Cognition meets le Corbusier—Cognitive principles of architectural design. Spatial Cognition III. Lecture notes in artificial intelligence. Springer, Berlin, pp 112–126Google Scholar
  42. 42.
    Yu AJ, Dayan P (2005) Uncertainty, neuromodulation, and attention. Neuron 46:681–692CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Dimitri Volchenkov
    • 1
  • Jonathan Helbach
    • 2
  • Marko Tscherepanow
    • 2
  • Sina Kühnel
    • 3
  1. 1.Faculty of PhysicsBielefeld UniversityBielefeldGermany
  2. 2.Technical FacultyBielefeld UniversityBielefeldGermany
  3. 3.Physiological PsychologyBielefeld UniversityBielefeldGermany

Personalised recommendations