Perception of Symmetries in Drawings of Graphs

Symmetry is an important factor in human perception in general, as well as in the visualization of graphs in particular. There are three main types of symmetry: reflective, translational, and rotational. We report the results of a human subjects experiment to determine what types of symmetries are more salient in drawings of graphs. We found statistically significant evidence that vertical reflective symmetry is the most dominant (when selecting among vertical reflective, horizontal reflective, and translational). We also found statistically significant evidence that rotational symmetry is affected by the number of radial axes (the more, the better), with a notable exception at four axes.Comment: Appears in the Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD 2018

Aesthetic Preferences in Mathematics: a Case Study

Although mathematicians often use it, mathematical beauty is a philosophically challenging concept. How can abstract objects be evaluated as beautiful? Is this related to the way we visualise them? Using a case study from graph theory (the highly symmetric Petersen graph), this paper tries to analyse aesthetic preferences in mathematical practice and to distinguish genuine aesthetic from epistemic or practical judgements. It argues that, in making aesthetic judgements, mathematicians may be responding to a combination of perceptual properties of visual representations and mathematical properties of abstract structures; the latter seem to carry greater weight. Mathematical beauty thus primarily involves mathematicians' sensitivity to aesthetics of the abstract

A parent-centered radial layout algorithm for interactive graph visualization and animation

We have developed (1) a graph visualization system that allows users to explore graphs by viewing them as a succession of spanning trees selected interactively, (2) a radial graph layout algorithm, and (3) an animation algorithm that generates meaningful visualizations and smooth transitions between graphs while minimizing edge crossings during transitions and in static layouts. Our system is similar to the radial layout system of Yee et al. (2001), but differs primarily in that each node is positioned on a coordinate system centered on its own parent rather than on a single coordinate system for all nodes. Our system is thus easy to define recursively and lends itself to parallelization. It also guarantees that layouts have many nice properties, such as: it guarantees certain edges never cross during an animation. We compared the layouts and transitions produced by our algorithms to those produced by Yee et al. Results from several experiments indicate that our system produces fewer edge crossings during transitions between graph drawings, and that the transitions more often involve changes in local scaling rather than structure. These findings suggest the system has promise as an interactive graph exploration tool in a variety of settings

Aesthetic Preferences in Mathematics: a Case Study

Although mathematicians often use it, mathematical beauty is a philosophically challenging concept. How can abstract objects be evaluated as beautiful? Is this related to the way we visualise them? Using a case study from graph theory (the highly symmetric Petersen graph), this paper tries to analyse aesthetic preferences in mathematical practice and to distinguish genuine aesthetic from epistemic or practical judgements. It argues that, in making aesthetic judgements, mathematicians may be responding to a combination of perceptual properties of visual representations and mathematical properties of abstract structures; the latter seem to carry greater weight. Mathematical beauty thus primarily involves mathematicians' sensitivity to aesthetics of the abstract

Method Meditation: An Experimental Demonstration of Systemization in Architecture

Method Meditation is an architectural design method developed during my exploration of systemization in the design process. Systems have been used throughout architectural history in an attempt to create space that can affect an occupant exactly the way the architect intended. However, these attempts have had inconsistent outcomes. This inconsistency has been attributed to several factors, from the variety to individual experiences that skew an observer’s viewpoint, to the lack of provable, causal relationships between environment and behavior. Due to these obstacles, other designers have used systems not to create perfect results, but to push their designs to new extents, and to produce unprecedented outcomes. To explore the relationship between systemization and design, I create my own method that would further incorporate the occupant in the design process, testing whether more thorough collaboration between the architect and occupant could produce a more desirable result. To do so, I examined the design preferences of thirty participants, twenty of whom are outside of the architectural field. The participants answered questions on two separate surveys that asked for preferences based on sixty two-dimensional illustrations. These illustrations are based in part on the work of Christopher Alexander, a proponent of systemization as a means of better design. The results of these surveys showed discrepancies between the choices of the participants within, and outside, of the architectural profession. Though the scope of this method is limited, its findings suggest the possible benefits of a closer relationship between the architect and occupants during the design process

Visualization of semantic similarity

No abstract availabl