Complex-Logarithmic Views and Map Warping

We are living in a very complex world. The data we are interacting with in these days of the computer age is often very detailed. It is also often hierarchically organized, with an increasing number of hierarchical steps and orders of magnitudes available, and therefore contains very small interesting parts in very large overall contexts.

The rapid increase in computing power, while being one of the reasons for the explosion in complex data we have to deal with, also offers a great opportunity to aid us in the great undertaking of understanding our complex world. In connection with modern interface technology, especially with graphical displays, it becomes the most exciting extension of our brains to date.

This work delves into the subdiscipline of distortion oriented detail-in-context techniques, the art and science of helping an observer to cope with the richness of data by magnifying important parts while shrinking the overall overview. Common distortion techniques from this field like fisheye mappings and perspective approaches have somehow failed to be able to deal with extreme differences in scale of Euclidean information. The reason for that seems to lie in the introduction of anisotropic compression in all common mapping functions, which squishes information together until it is not recognizable anymore.

This thesis presents the results of the exploration of mapping and interaction approaches, driven amongst others by the mathematical field of complex analysis, by brain research, and the analysis of artistic examples.