An alternative route to the Mandelbrot set: connecting idiosyncratic digital representations for undergraduates

Hypercomputing the Mandelbrot Set?

The Mandelbrot set is an extremely well-known mathematical object that can be described in a quite simple way but has very interesting and non-trivial properties. This paper surveys some results that are known concerning the (non-)computability of the set. It considers two models of decidability over the reals (which are treated much more thoroughly and technically in [1], [2], [3] and [4] amon...

Extension of the Douady-Hubbard's Theorem on Connectedness of the Mandelbrot Set to Symmetric Polynimials

The Role of Digital Technologies as an Alternative for Face-to-Face Knee Rehabilitation: A Systematic Review

Background: Digital technologies, including mobile applications, websites, and wearable devices, like smartwatches are among the newest approaches in prevention, care, and treatment studies; they could provide public access to high-quality rehabilitation services. The current review study aimed to evaluate the effects of digital technologies for enhancing physical activity, as well as improving...

Is the Mandelbrot set computable?

We discuss the question whether the Mandelbrot set is computable. The computability notions which we consider are studied in computable analysis and will be introduced and discussed. We show that the exterior of the Mandelbrot set, the boundary of the Mandelbrot set, and the hyperbolic components satisfy certain natural computability conditions. We conclude that the two–sided distance function ...

Instability of the Mandelbrot Set

für Naturforschung in cooperation with the Max Planck Society for the Advancement of Science under a Creative Commons Attribution 4.0 International License. Dieses Werk wurde im Jahr 2013 vom Verlag Zeitschrift für Naturforschung in Zusammenarbeit mit der Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V. digitalisiert und unter folgender Lizenz veröffentlicht: Creative Commons Namen...