Calculating Voronoi Diagrams Using Simple Chemical Reactions

2015 ◽  
Vol 25 (01) ◽  
pp. 1540003 ◽  
Author(s):  
Ben De Lacy Costello
Keyword(s):  
Chemical Reactions ◽  
Voronoi Diagrams ◽  
Computation Time ◽  
Cross Reactivity ◽  
Relative Strength ◽  
Specific Chemical ◽  
Natural Systems ◽  
Simple Chemical ◽  
Chemical Inputs ◽  
Pattern Forming

This paper overviews work on the use of simple chemical reactions to calculate Voronoi diagrams and undertake other related geometric calculations. This work highlights that this type of specialised chemical processor is a model example of a parallel processor. For example increasing the complexity of the input data within a given area does not increase the computation time. These processors are also able to calculate two or more Voronoi diagrams in parallel. Due to the specific chemical reactions involved and the relative strength of reaction with the substrate (and cross-reactivity with the products) these processors are also capable of calculating Voronoi diagrams sequentially from distinct chemical inputs. The chemical processors are capable of calculating a range of generalised Voronoi diagrams (either from circular drops of chemical or other geometric shapes made from adsorbent substrates soaked in reagent) , skeletonisation of planar shapes and weighted Voronoi diagrams (e.g., additively weighted Voronoi diagrams, Multiplicitavely weighted Crystal growth Voronoi diagrams). The paper will also discuss some limitations of these processors. These chemical processors constitute a class of pattern forming reactions which have parallels with those observed in natural systems. It is possible that specialised chemical processors of this general type could be useful for synthesising functional structured materials.

CHEMICAL TESSELLATIONS — RESULTS OF BINARY AND TERTIARY REACTIONS BETWEEN METAL IONS AND FERRICYANIDE OR FERROCYANIDE LOADED GELS

2010 ◽  
Vol 20 (07) ◽  
pp. 2241-2252 ◽  
Author(s):  
B. P. J. DE LACY COSTELLO ◽  
I. JAHAN ◽  
P. HAMBIDGE ◽  
K. LOCKING ◽  
D. PATEL ◽  
...  
Keyword(s):  
Metal Ions ◽  
Voronoi Diagram ◽  
Metal Salt ◽  
Voronoi Diagrams ◽  
Reaction Rates ◽  
Cross Reactivity ◽  
Diffusion Reaction ◽  
Reactive Metal ◽  
Simple Chemical ◽  
Pattern Forming

In our recent letter [de Lacy Costello et al., 2009] we described the formation of spontaneous complex tessellations of the plane constructed in simple chemical reactions between drops of metal salts and ferricyanide or ferrocyanide loaded gels. In this paper, we provide more examples of binary tessellations and extend our analysis to tessellations constructed via tertiary mixtures of reactants. We also provide a classification system which describes the tessellation based on the reactivity of the metal salt with the substrate and also the cross-reactivity of the primary products. This results in balanced tessellations where both reactants have equal reactivity or unbalanced tessellations where one reactant has a lower reactivity with the gel. The products can also be partially or fully cross reactive which gives a highly complex tessellation. The tessellations are made up of colored cells (corresponding to different metal ferricyanides or ferrocyanides) separated by bisectors of low precipitate concentration. The tessellations constructed by these reactions constitute generalized Voronoi diagrams. In the case of certain binary or tertiary combinations of reactants where the diffusion/reaction rates differ, then multiplicatively weighted crystal growth Voronoi diagrams are constructed. Where one reactant has limited or no reactivity with the gel (or the products are cross reactive) then the fronts originating from the reactive metal ions cross the fronts originating from the partially reactive metal ions. The fronts can annihilate in the formation of a second Voronoi diagram relating to the relative positions of the reactive drops. Therefore, two or more generalised or weighted Voronoi diagrams can be calculated in parallel by these simple chemical systems. However when these reactions were used to calculate an additively weighted Voronoi diagram (the reaction was initiated at different time intervals) the diagram constructed did not correspond to the theoretical calculation. We use the failure of these reactions to construct an additively weighted Voronoi diagram to prove a mechanism of substrate competition for bisector formation. These tessellations are an important class of pattern forming reactions and are useful in modeling natural pattern forming phenomena in addition to being a great resource for scientific demonstrations.

scholarly journals Sequential Voronoi Diagram Calculations using Simple Chemical Reactions

2011 ◽  
Vol 3 (3) ◽  
pp. 29-41
Author(s):  
B. P. J. de Lacy Costello ◽  
I. Jahan ◽  
A. Adamatzky
Keyword(s):  
Voronoi Diagram ◽  
Chemical Reactions ◽  
Voronoi Diagrams ◽  
Cross Reactivity ◽  
Potassium Ferricyanide ◽  
Potassium Ferrocyanide ◽  
Metal Salts ◽  
Unconventional Computing ◽  
Simple Chemical ◽  
Calculation Results

In the authors’ recent paper (de Lacy Costello et al., 2010) the authors described the formation of complex tessellations of the plane arising from the various reactions of metal salts with potassium ferricyanide and ferrocyanide loaded gels. In addition to producing colourful tessellations these reactions are naturally computing generalised Voronoi diagrams of the plane. The reactions reported previously were capable of the calculation of three distinct Voronoi diagrams of the plane. As diffusion coupled with a chemical reaction is responsible for the calculation then this is achieved in parallel. Thus an increase in the complexity of the data input does not utilise additional computational resource. Additional benefits of these chemical reactions are that a permanent record of the Voronoi diagram calculation (in the form of precipitate free bisectors) is achieved, so there is no requirement for further processing to extract the calculation results. Previously it was assumed that the permanence of the results was also a potential drawback which limited reusability. This paper presents new data which shows that sequential Voronoi diagram calculations can be performed on the same chemical substrate. This is dependent on the reactivity of the original reagent and the cross reactivity of the secondary reagent with the primary product. The authors present the results from a number of binary combinations of metal salts on both potassium ferricyanide and potassium ferrocyanide substrates. The authors observe three distinct mechanisms whereby secondary sequential Voronoi diagrams can be calculated. In most cases the result was two interpenetrating permanent Voronoi diagrams. This is interesting from the perspective of mapping the capability of unconventional computing substrates. But also in the study of natural pattern formation per se.

Reactions

2011 ◽  
Author(s):  
Peter Atkins
Keyword(s):  
Chemical Reactions ◽  
Molecular Level ◽  
Chemical Processes ◽  
Chemical Formula ◽  
Complex Processes ◽  
Full Color ◽  
Chemistry Textbooks ◽  
Simple Chemical ◽  
The Subject ◽  
Solid Form

Illustrated with remarkable new full-color images--indeed, one or more on every page--and written by one of the world's leading authorities on the subject, Reactions offers a compact, pain-free tour of the inner workings of chemistry. Reactions begins with the chemical formula almost everyone knows--the formula for water, H2O--a molecule with an "almost laughably simple chemical composition." But Atkins shows that water is also rather miraculous--it is the only substance whose solid form is less dense than its liquid (hence ice floats in water)--and incredibly central to many chemical reactions, as it is an excellent solvent, being able to dissolve gases and many solids. Moreover, Atkins tells us that water is actually chemically aggressive, and can react with and destroy the compounds dissolved in it, and he shows us what happens at the molecular level when water turns to ice--and when it melts. Moving beyond water, Atkins slowly builds up a toolkit of basic chemical processes, including precipitation (perhaps the simplest of all chemical reactions), combustion, reduction, corrosion, electrolysis, and catalysis. He then shows how these fundamental tools can be brought together in more complex processes such as photosynthesis, radical polymerization, vision, enzyme control, and synthesis. Peter Atkins is the world-renowned author of numerous best-selling chemistry textbooks for students. In this crystal-clear, attractively illustrated, and insightful volume, he provides a fantastic introductory tour--in just a few hundred colorful and lively pages - for anyone with a passing or serious interest in chemistry.

scholarly journals Physical principles of membrane organization

1980 ◽  
Vol 13 (2) ◽  
pp. 121-200 ◽  
Author(s):  
J. N. Israelachvili ◽  
S. Marčelja ◽  
R. G. Horn
Keyword(s):  
Chemical Reactions ◽  
Nerve Conduction ◽  
Energy Transduction ◽  
Molecular Organization ◽  
Cellular Structures ◽  
Cellular Activity ◽  
Simple Chemical ◽  
Unicellular Organisms ◽  
Almost All ◽  
Physical Principles

Membranes are the most common cellular structures in both plants and animals. They are now recognized as being involved in almost all aspects of cellular activity ranging from motility and food entrapment in simple unicellular organisms, to energy transduction, immunorecognition, nerve conduction and biosynthesis in plants and higher organisms. This functional diversity is reflected in the wide variety of lipids and particularly of proteins that compose different membranes. An understanding of the physical principles that govern the molecular organization of membranes is essential for an understanding of their physiological roles since structure and function are much more interdependent in membranes than in, say, simple chemical reactions in solution. We must recognize, however, that the word ‘understanding’ means different things in different disciplines, and nowhere is this more apparent than in this multidisciplinary area where biology, chemistry and physics meet.

scholarly journals The influence of velocity field on simple chemical reactions in viscous flow

2019 ◽  
Vol 94 (4) ◽  
pp. 045002 ◽  
Author(s):  
A R Karimov ◽  
M A Taleisnik ◽  
T V Savenkova ◽  
L M Aksenova
Keyword(s):  
Velocity Field ◽  
Viscous Flow ◽  
Chemical Reactions ◽  
Simple Chemical
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