Related papers: Visual Explorations of Dynamics: the Standard Map
Area preserving maps provide the simplest and most accurate means to visualize and quantify the behavior of nonlinear systems. Convenience of the mapping equations of motion for investigation of transition to chaotic behavior in dynamics of…
A relevant problem in dynamics is to characterize how deterministic systems may exhibit features typically associated to stochastic processes. A widely studied example is the study of (normal or anomalous) transport properties for…
We describe a newly-developed, free, browser-based application, for the interactive exploration of the dynamic geometry of Poncelet families of triangles. The main focus is on responsive display of the beauteous loci of centers of such…
This paper describes a system to support the visual exploration of Open Data. During his/her interactive experience with the graphics, the user can easily store the current complete state of the visualization application (called a…
Stickiness is a well known phenomenon in which chaotic orbits expend an expressive amount of time in specific regions of the chaotic sea. This phenomenon becomes important when dealing with area-preserving open systems because, in this…
The Persint program is designed for the three-dimensional representation of objects and for the interfacing and access to a variety of independent applications, in a fully interactive way. Facilities are provided for the spatial navigation…
In this note, we offer a palatable introduction to the field of arithmetic dynamics. That is, we study the patterns that arise when iterating a polynomial map. This note is accessible to those who have taken an introductory proof based…
Stability is a fundamental notion in dynamical systems and control theory that, traditionally understood, describes asymptotic behavior of solutions around an equilibrium point. This notion may be characterized abstractly as continuity of a…
The appearance of the world varies dramatically not only from place to place but also from hour to hour and month to month. Every day billions of images capture this complex relationship, many of which are associated with precise time and…
This paper presents evomap, a Python package for dynamic mapping. Mapping methods are widely used across disciplines to visualize relationships among objects as spatial representations, or maps. However, most existing statistical software…
Text-to-image generative models can be tremendously valuable in supporting creative tasks by providing inspirations and enabling quick exploration of different design ideas. However, one common challenge is that users may still not be able…
In this paper, we present an approach to enhance and improve the current normal map rendering technique. Our algorithm is based on semi-discrete Optimal Mass Transportation (OMT) theory and has a solid theoretical base. The key difference…
A famous aspect of discrete dynamical systems defined by area-preserving maps is the physical interpretation of stochastic transitions occurring locally which manifest themselves through the destruction of invariant KAM curves and the local…
Real-world graphs often contain spatio-temporal information and evolve over time. Compared with static graphs, spatio-temporal graphs have very different characteristics, presenting more significant challenges in data volume, data velocity,…
This paper explores visual motion-based invariants, resulting in a new instantaneous domain where: a) the stationary environment is perceived as unchanged, even as the 2D images undergo continuous changes due to camera motion, b) obstacles…
Topological methods for data analysis present opportunities for enforcing certain invariances of broad interest in computer vision, including view-point in activity analysis, articulation in shape analysis, and measurement invariance in…
Software visualization helps to comprehend the system by providing a vivid illustration. The developers, as well as the analysts, can have a glance over the total system to understand the basic changes over time from a high-level point of…
Symbolic dynamics is a coarse-grained description of dynamics. By taking into account the ``geometry'' of the dynamics, it can be cast into a powerful tool for practitioners in nonlinear science. Detailed symbolic dynamics can be developed…
A web application prototype is described, aimed at the generation of synthetic seismograms for user-defined earthquake models. The web application graphical user interface hides the complexity of the underlying computational engine, which…
Video editing is a creative and complex endeavor and we believe that there is potential for reimagining a new video editing interface to better support the creative and exploratory nature of video editing. We take inspiration from latent…