ON SIMULTANEOUS CONSTRUCTION OF VORONOI DIAGRAM AND DELAUNAY TRIANGULATION BY PHYSARUM POLYCEPHALUM

Abstract

We experimentally demonstrate that both Voronoi diagram and its dual graph Delaunay triangulation are simultaneously constructed — for specific conditions — in cultures of plasmodium, a vegetative state of Physarum polycephalum. Every point of a given planar data set is represented by a tiny mass of plasmodium. The plasmodia spread from their initial locations but, in certain conditions, stop spreading when they encounter plasmodia originated from different locations. Thus space loci not occupied by the plasmodia represent edges of Voronoi diagram of the given planar set. At the same time, the plasmodia originating at neighboring locations form merging protoplasmic tubes, where the strongest tubes approximate Delaunay triangulation of the given planar set. The problems are solved by plasmodium only for limited data sets, however the results presented lay a sound ground for further investigations.

Influences on the formation and evolution of Physarum polycephalum inspired emergent transport networks

“…In recent years, there has been a wealth of research into its computational abilities, prompted by Nakagaki et al who initially reported the ability of Physarum to solve path planning problems (Nakagaki et al 2000). Subsequent research has confirmed and broadened the range of abilities to spatial representations of various graph problems (Nakagaki et al 2004b;Shirakawa et al 2009;Adamatzky 2008b), combinatorial optimisation problems (Aono and Hara 2007), construction of logic gates (Tsuda et al 2004) and logical machines (Adamatzky 2007), and as a means to achieve distributed robotic control (Tsuda et al 2007) and robotic amoebic movement (Ishiguro et al 2006).…”

Characteristics of Pattern Formation and Evolution in Approximations of Physarum Transport Networks

“…In recent years there has been a wealth of research into its computational abilities, prompted by Nakagaki et al, who reported the ability of Physarum to solve path planning problems [38]. Subsequent research has confirmed this and broadened the range of abilities to spatial representations of various graph problems [3,37,43] and combinatorial optimization problems [6], to construction of logic gates [49] and logical machines [2,5], and to the achievement distributed robotic control [50], robotic manipulation [4], and robotic amoebic movement [22].…”

Sounds synthesis with slime mould of Physarum Polycephalum

“…In practice we sample 100 measurements in one second and then these values are averaged. Furthermore, in order to compress data worth of several days of activity into data suitable to produce a few minutes of sound, we process the electric potentials from electrodes e 1 …e 8 , where (C) = 1 if predicate C is true and 0 otherwise. Also, voltage values were capped in a range between 40mV to 40mV, which corresponds to a normal range of plasmodium activity, and yet this removes potential interference from nearby electrical equipment.…”

“…Its optimal foraging and reaction to attracting (e.g., food and humidity) and repelling (e.g., light and salt) sources makes it an ideal candidate for researching into biological unconventional computers. It has been already demonstrated that computing devices based on this plasmodium [5] were capable of solving difficult classic computational problems such as: approximation of shortest path [6] , planar proximity graphs [7] , voronoi diagram [8] , execution of basic logical operations [9,10] , spatial logic and process algebra [11] . Plasmodium of Physarum is experimentally proved to be an original and efficient micromanipulator controlled by light [12] .…”