The densest packings of N unit squares in a torus are studied using analytical methods as well as simulated annealing. A rich array of dense packing solutions are found: density-one packings when N is the sum of two square integers; a family of 'gapped bricklayer' Bravais lattice solutions with density N/(N + 1); and some surprising non-Bravais lattice configurations, including lattices of holes as well as a configuration for N = 23 in which not all squares share the same orientation. The entropy of some of these configurations and the frequency and orientation of density-one solutions as are discussed.
This chapter explores the potential of play in relation to community-based civic science research using DIY scientific tools made possible by the Public Laboratory for Open Technology and Science (Public Lab).It discusses projects and approaches that the Public Lab has developed since its launch in 2010 to facilitate meaningful civic science collaboration.This includes a focus on narrative forms to connect participants to science research, relying on a spontaneous, playful emergence of collaborative activity rather than pre-developed forms of gamification to allow the incentives for participation to be intrinsic to the nature of the activity.This transforms the practice of scientific research and civic engagement into something that is both effective and ultimately enjoyable and productive, for all of those involved.
In the last decade, digital media technologies and developments have given rise to exciting new forms of ludic, or playful, engagements of citizens in cultural and societal issues. From the Occupy movement to playful city-making to the gameful designs of the Obama 2008 and Trump 2016 presidential campaigns, and the rise of citizen science and ecological games, this book shows how play is a key theoretical, methodological, and practical principle for comprehending such new forms of civic engagement in a mediatized culture. The Playful Citizen explores how and through what media we are becoming more playful as citizens and how this manifests itself in our ways of doing, living, and thinking. We offer a pluralistic answer to such questions by bringing together scholars from different fields such as game and play studies, social sciences, and media and culture studies.
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