TL;DR
This paper investigates the space of wiggles, which are embedded plane curves as attractors of iterated function systems, and demonstrates that this space contains disconnected regions called wiggle islands.
Contribution
It proves that the space of wiggles is disconnected, revealing the existence of wiggle islands, a novel topological feature in this context.
Findings
The space of wiggles is disconnected.
Existence of wiggle islands within the space.
Wiggles are attractors of specific iterated function systems.
Abstract
A wiggle is an embedded curve in the plane that is the attractor of an iterated function system associated to a complex parameter z. We show the space of wiggles is disconnected -- i.e. there is a wiggle island.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Quantum chaos and dynamical systems · Advanced Differential Equations and Dynamical Systems