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Journal articles on the topic 'Diagrammes de voronoi'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 January 2025

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1

Mumm, Michael. "Voronoi Diagrams." Mathematics Enthusiast 1, no. 2 (2004): 44–55. http://dx.doi.org/10.54870/1551-3440.1009.

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2

Sugihara, K. "Approximation of Generalized Voronoi Diagrams by Ordinary Voronoi Diagrams." CVGIP: Graphical Models and Image Processing 55, no. 6 (1993): 522–31. http://dx.doi.org/10.1006/cgip.1993.1039.

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3

MEHLHORN, KURT, STEFAN MEISER, and RONALD RASCH. "FURTHEST SITE ABSTRACT VORONOI DIAGRAMS." International Journal of Computational Geometry & Applications 11, no. 06 (2001): 583–616. http://dx.doi.org/10.1142/s0218195901000663.

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Voronoi diagrams were introduced by R. Klein as a unifying approach to Voronoi diagrams. In this paper we study furthest site abstract Voronoi diagrams and give a unified mathematical and algorithmic treatment for them. In particular, we show that furthest site abstract Voronoi diagrams are trees, have linear size, and that, given a set of n sites, the furthest site abstract Voronoi diagram can be computed by a randomized algorithm in expected time O(n log n).

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4

Bormashenko, Edward, Irina Legchenkova, Mark Frenkel, Nir Shvalb, and Shraga Shoval. "Voronoi Entropy vs. Continuous Measure of Symmetry of the Penrose Tiling: Part I. Analysis of the Voronoi Diagrams." Symmetry 13, no. 9 (2021): 1659. http://dx.doi.org/10.3390/sym13091659.

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A continuous measure of symmetry and the Voronoi entropy of 2D patterns representing Voronoi diagrams emerging from the Penrose tiling were calculated. A given Penrose tiling gives rise to a diversity of the Voronoi diagrams when the centers, vertices, and the centers of the edges of the Penrose rhombs are taken as the seed points (or nuclei). Voronoi diagrams keep the initial symmetry group of the Penrose tiling. We demonstrate that the continuous symmetry measure and the Voronoi entropy of the studied sets of points, generated by the Penrose tiling, do not necessarily correlate. Voronoi diag

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5

Boots, Barry, and Narushige Shiode. "Recursive Voronoi Diagrams." Environment and Planning B: Planning and Design 30, no. 1 (2003): 113–24. http://dx.doi.org/10.1068/b12984.

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This paper introduces procedures involving the recursive construction of Voronoi diagrams and Delaunay tessellations. In such constructions, Voronoi and Delaunay concepts are used to tessellate an object space with respect to a given set of generators and then the construction is repeated every time with a new generator set, which comprises members selected from the previous generator set plus features of the current tessellation. Such constructions are shown to provide an integrating conceptual framework for a number of disparate procedures, as well as extending the existing functionality of

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6

Canny, John, and Bruce Donald. "Simplified Voronoi diagrams." Discrete & Computational Geometry 3, no. 3 (1988): 219–36. http://dx.doi.org/10.1007/bf02187909.

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7

AICHHOLZER, OSWIN, FRANZ AURENHAMMER, DANNY Z. CHEN, D. T. LEE, and EVANTHIA PAPADOPOULOU. "SKEW VORONOI DIAGRAMS." International Journal of Computational Geometry & Applications 09, no. 03 (1999): 235–47. http://dx.doi.org/10.1142/s0218195999000169.

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On a tilted plane T in three-space, skew distances are defined as the Euclidean distance plus a multiple of the signed difference in height. Skew distances may model realistic environments more closely than the Euclidean distance. Voronoi diagrams and related problems under this kind of distances are investigated. A relationship to convex distance functions and to Euclidean Voronoi diagrams for planar circles is shown, and is exploited for a geometric analysisis and a plane-sweep construction of Voronoi diagrams on T. An output-sensitive algorithm running in time O(n log h) is developed, where

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8

Boissonnat, Jean-Daniel, Frank Nielsen, and Richard Nock. "Bregman Voronoi Diagrams." Discrete & Computational Geometry 44, no. 2 (2010): 281–307. http://dx.doi.org/10.1007/s00454-010-9256-1.

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9

Allen, Sarah R., Luis Barba, John Iacono, and Stefan Langerman. "Incremental Voronoi Diagrams." Discrete & Computational Geometry 58, no. 4 (2017): 822–48. http://dx.doi.org/10.1007/s00454-017-9943-2.

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10

Nielsen, Frank. "On Voronoi Diagrams on the Information-Geometric Cauchy Manifolds." Entropy 22, no. 7 (2020): 713. http://dx.doi.org/10.3390/e22070713.

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We study the Voronoi diagrams of a finite set of Cauchy distributions and their dual complexes from the viewpoint of information geometry by considering the Fisher-Rao distance, the Kullback-Leibler divergence, the chi square divergence, and a flat divergence derived from Tsallis entropy related to the conformal flattening of the Fisher-Rao geometry. We prove that the Voronoi diagrams of the Fisher-Rao distance, the chi square divergence, and the Kullback-Leibler divergences all coincide with a hyperbolic Voronoi diagram on the corresponding Cauchy location-scale parameters, and that the dual

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11

SAJI, KENTARO. "BIFURCATIONS OF VORONOI DIAGRAMS AND ITS APPLICATION TO BRAID THEORY." Journal of Knot Theory and Its Ramifications 13, no. 02 (2004): 249–57. http://dx.doi.org/10.1142/s0218216504003111.

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We study bifurcations of Voronoi diagrams on the plane. The generic bifurcations of Voronoi diagrams for moving points are classified into four types. A braid has an associated family of Voronoi diagrams. If we admit only three types among four in the associated generic family of Voronoi diagrams, the braid type reduces to a braid with k half twists for some integer k.

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12

DE LACY COSTELLO, BEN, NORMAN RATCLIFFE, ANDREW ADAMATZKY, ALEXEY L. ZANIN, ANDREAS W. LIEHR, and HANS-GEORG PURWINS. "THE FORMATION OF VORONOI DIAGRAMS IN CHEMICAL AND PHYSICAL SYSTEMS: EXPERIMENTAL FINDINGS AND THEORETICAL MODELS." International Journal of Bifurcation and Chaos 14, no. 07 (2004): 2187–210. http://dx.doi.org/10.1142/s021812740401059x.

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The work discusses the formation of Voronoi diagrams in spatially extended nonlinear systems taking experimental and theoretical results into account. Concerning experimental systems a number of chemical systems used previously as prototype chemical processors and a barrier gas-discharge system are investigated. Although the underlying microscopic processes are very different, both types of systems show self-organized Voronoi diagrams for suitable parameters. Indeed certain chemical systems exhibit Voronoi diagrams as an output state for two distinct sets of parameters one that corresponds to

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13

SUGIHARA, KOKICHI. "VORONOI DIAGRAMS IN A RIVER." International Journal of Computational Geometry & Applications 02, no. 01 (1992): 29–48. http://dx.doi.org/10.1142/s0218195992000032.

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A new generalized Voronoi diagram is defined on the surface of a river with uniform flow; a point belongs to the territory of a site if and only if a boat starting from the site can reach the point faster than a boat starting from any other site. If the river runs slower than the boat, the Voronoi diagram has the same topological structure as the ordinary Voronoi diagram, and hence can be constructed from the ordinary Voronoi diagram by a certain transformation. If the river runs faster than the boat, on the other hand, the topological structure of the diagram becomes different from the ordina

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14

De Lacy Costello, Ben. "Calculating Voronoi Diagrams Using Simple Chemical Reactions." Parallel Processing Letters 25, no. 01 (2015): 1540003. http://dx.doi.org/10.1142/s0129626415400034.

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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

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15

Pokojski, Wojciech, and Paulina Pokojska. "Voronoi diagrams – inventor, method, applications." Polish Cartographical Review 50, no. 3 (2018): 141–50. http://dx.doi.org/10.2478/pcr-2018-0009.

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Abstract The article presents the person and works of Georgy Voronoi (1868-1908), the inventor of an original method of diagrams, a student of the famous mathematician Andrey Markov. Georgy Voronoi graduated from the Department of Physics and Mathematics at the University of St. Petersburg, and subsequently worked as a professor of mathematics at the Imperial University of Warsaw. One of his students was the future outstanding Polish mathematician Wacław Sierpiński. In his brief lifetime G. Voronoi published several important scientific articles on number theory. In an almost 100 page paper in

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16

Ustimenko, V. "On small world non-Sunada twins and cellular Voronoi diagrams." Algebra and Discrete Mathematics 30, no. 1 (2020): 118–42. http://dx.doi.org/10.12958/adm1343.

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Special infinite families of regular graphs of unbounded degree and of bounded diameter (small world graphs) are considered. Two families of small world graphs Gi and Hi form a family of non-Sunada twins if Gi and Hi are isospectral of bounded diameter but groups Aut(Gi) and Aut(Hi) are nonisomorphic. We say that a family of non-Sunada twins is unbalanced if each Gi is edge-transitive but each Hi is edge-intransitive. If all Gi and Hi are edge-transitive we have a balanced family of small world non-Sunada twins. We say that a family of non-Sunada twins is strongly unbalanced if each Gi is edge

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17

BOHLER, CECILIA, and ROLF KLEIN. "ABSTRACT VORONOI DIAGRAMS WITH DISCONNECTED REGIONS." International Journal of Computational Geometry & Applications 24, no. 04 (2014): 347–72. http://dx.doi.org/10.1142/s0218195914600115.

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Abstract Voronoi diagrams, AVDs for short, are based on bisecting curves enjoying simple combinatorial properties, rather than on the geometric notions of sites and distance. They serve as a unifying concept. Once the bisector system of any concrete type of Voronoi diagram is shown to fulfill the AVD axioms, structural results and efficient algorithms become available without further effort; for example, the first optimal algorithms for constructing nearest Voronoi diagrams of disjoint convex objects, or of line segments under the Hausdorff metric, have been obtained this way. One of these axi

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18

Mazón, M., and T. Recio. "Voronoi Diagrams on orbifolds." Computational Geometry 8, no. 5 (1997): 219–30. http://dx.doi.org/10.1016/s0925-7721(96)00017-x.

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19

Nilforoushan, Z., A. Mohades, M. M. Rezaii, and A. Laleh. "3D hyperbolic Voronoi diagrams." Computer-Aided Design 42, no. 9 (2010): 759–67. http://dx.doi.org/10.1016/j.cad.2010.04.005.

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20

Edelsbrunner, Herbert, and Raimund Seidel. "Voronoi diagrams and arrangements." Discrete & Computational Geometry 1, no. 1 (1986): 25–44. http://dx.doi.org/10.1007/bf02187681.

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21

Klein, Rolf, Elmar Langetepe, and Zahra Nilforoushan. "Abstract Voronoi diagrams revisited." Computational Geometry 42, no. 9 (2009): 885–902. http://dx.doi.org/10.1016/j.comgeo.2009.03.002.

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22

Cheong, Otfried, Hazel Everett, Marc Glisse, et al. "Farthest-polygon Voronoi diagrams." Computational Geometry 44, no. 4 (2011): 234–47. http://dx.doi.org/10.1016/j.comgeo.2010.11.004.

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23

Reitsma, René, and Stanislav Trubin. "Information Space Partitioning Using Adaptive Voronoi Diagrams." Information Visualization 6, no. 2 (2007): 123–38. http://dx.doi.org/10.1057/palgrave.ivs.9500152.

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In this paper, we present and evaluate a Voronoi method for partitioning continuous information spaces. We define the formal characteristics of the problem and discuss several well-known partitioning methods and approaches. We submit that although they all partially solve the problem, they all have shortcomings. As an alternative, we offer an approach based on an adaptive version of the multiplicatively weighted Voronoi diagram. The diagram is ‘adaptive’ because it is computed backwards; that is, the generators' weights are treated as dependent rather than independent variables. We successfull

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24

Weydemann, Leonard, Christian Clemenz, and Clemens Preisinger. "On the Structural Properties of Voronoi Diagrams." KoG, no. 25 (2021): 72–77. http://dx.doi.org/10.31896/k.25.8.

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A Voronoi diagram is a tessellation technique, which subdivides space into regions in proximity to a given set of objects called seeds. Patterns emerging naturally in biological processes (for example, in cell tissue) can be modelled in a biomimicry process via Voronoi diagrams. As they originate in nature, we investigate the physical properties of such patterns to determine whether they are optimal given the constraints imposed by surrounding geometry and natural forces. This paper describes under what circumstances the Voronoi tessellation has optimal (structural) properties by surveying rec

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25

Reddy, Tyler, Ross Hemsley, Edd Edmondson, Nikolai Nowaczyk, Joe Pitt-Francis, and Mark S. P. Sansom. "VENI, VIDI, Voronoi: Attacking Viruses with Spherical Voronoi Diagrams." Biophysical Journal 110, no. 3 (2016): 36a. http://dx.doi.org/10.1016/j.bpj.2015.11.263.

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26

Liu, Qingping, Xuesheng Zhao, Yuanzheng Duan, Mengmeng Qin, Wenlan Xie, and Wenbin Sun. "Dynamic Construction of Spherical Raster Voronoi Diagrams Based on Ordered Dilation." ISPRS International Journal of Geo-Information 13, no. 6 (2024): 202. http://dx.doi.org/10.3390/ijgi13060202.

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The Voronoi diagram on the Earth’s surface is a significant data model, characterized by natural proximity and dynamic stability, which has emerged as one of the most promising solutions for global spatial dynamic management and analysis. However, traditional algorithms for generating spherical raster Voronoi diagrams find it challenging to dynamically adjust the Voronoi diagram while maintaining precision and efficiency. The efficient and accurate construction of the spherical Voronoi diagram has become one of the bottleneck issues limiting its further large-scale application. To this end, th

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27

Frenkel, Mark, Irina Legchenkova, Nir Shvalb, Shraga Shoval, and Edward Bormashenko. "Voronoi Diagrams Generated by the Archimedes Spiral: Fibonacci Numbers, Chirality and Aesthetic Appeal." Symmetry 15, no. 3 (2023): 746. http://dx.doi.org/10.3390/sym15030746.

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Voronoi mosaics inspired by seed points placed on the Archimedes Spirals are reported. Voronoi (Shannon) entropy was calculated for these patterns. Equidistant and non-equidistant patterns are treated. Voronoi tessellations generated by the seeds located on the Archimedes spiral and separated by linearly growing radial distance demonstrate a switch in their chirality. Voronoi mosaics built from cells of equal size, which are of primary importance for the decorative arts, are reported. The pronounced prevalence of hexagons is inherent for the patterns with an equidistant and non-equidistant dis

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28

Carnasciali, Ana Maria dos Santos, Luciene Stamato Delazari, and Daniel Rodrigues dos Santos. "Determinação de áreas de abrangência de agência bancária pelo diagrama de Voronoi com obstáculos." Boletim de Ciências Geodésicas 17, no. 2 (2011): 200–217. http://dx.doi.org/10.1590/s1982-21702011000200003.

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Os diagramas de Voronoi permitem a subdivisão das regiões em um conjunto de áreas de abrangência, a fim de estabelecer relações de proximidades. Vários estudos foram realizados para a determinação de áreas de abrangência com o uso dos diagramas de Voronoi. Entretanto, ainda é necessário aprofundar as investigações com o desenvolvimento de novas proposições, com vistas à determinação de áreas de abrangência que se aproximem da realidade topográfica das cidades. Para tal, é necessário que sejam considerados os obstáculos, ou seja, barreiras lineares e fechadas. De acordo com a literatura consult

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29

Boonprong, Sornkitja, Nathapat Punturasan, Pariwate Varnakovida, and Wichien Prechathamwong. "Towards Sustainable Urban Mobility: Voronoi-Based Spatial Analysis of EV Charging Stations in Bangkok." Sustainability 16, no. 11 (2024): 4729. http://dx.doi.org/10.3390/su16114729.

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This study leverages the efficacy of Voronoi diagram theory within a mixed-methods approach to thoroughly examine the spatial distribution, service coverage, and optimal locations for expanding electric vehicle (EV) charging infrastructure in Bangkok. Drawing on data from field surveys and public data providers, our analysis unfolds in four key stages. Firstly, we delve into the spatial distribution of charging stations, scrutinizing density, proximity to various road types, and land use through the lens of Voronoi diagrams. Secondly, the application of Voronoi diagrams informs the evaluation

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30

Sang, E. T. K. "VORONOI DIAGRAMS WITHOUT BOUNDING BOXES." ISPRS Annals of Photogrammetry, Remote Sensing and Spatial Information Sciences II-2/W2 (October 19, 2015): 235–39. http://dx.doi.org/10.5194/isprsannals-ii-2-w2-235-2015.

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We present a technique for presenting geographic data in Voronoi diagrams without having to specify a bounding box. The method restricts Voronoi cells to points within a user-defined distance of the data points. The mathematical foundation of the approach is presented as well. The cell clipping method is particularly useful for presenting geographic data that is spread in an irregular way over a map, as for example the Dutch dialect data displayed in Figure 2. The automatic generation of reasonable cell boundaries also makes redundant a frequently used solution to this problem that requires da

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31

BILIUS, Laura-Bianca, and Stefan-Gheorghe PENTIUC. "Image Restoration using Voronoi Diagrams." Journal of Applied Computer Science & Mathematics 12, no. 2 (2018): 20–24. http://dx.doi.org/10.4316/jacsm.201802003.

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32

Perham, Arnold E., and Faustine L. Perham. "Voronoi Diagrams and Spring Rain." Mathematics Teacher 105, no. 2 (2011): 126–32. http://dx.doi.org/10.5951/mathteacher.105.2.0126.

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33

Chen, Danny Z., Ziyun Huang, Yangwei Liu, and Jinhui Xu. "On Clustering Induced Voronoi Diagrams." SIAM Journal on Computing 46, no. 6 (2017): 1679–711. http://dx.doi.org/10.1137/15m1044874.

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34

Sadahiro, Yukio, and Takashi Tominaga. "Accuracy of quantized Voronoi diagrams." International Journal of Geographical Information Science 20, no. 10 (2006): 1173–89. http://dx.doi.org/10.1080/13658810600816748.

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35

Barequet, Gill, Matthew T. Dickerson, and Robert L. Scot Drysdale. "2-Point site Voronoi diagrams." Discrete Applied Mathematics 122, no. 1-3 (2002): 37–54. http://dx.doi.org/10.1016/s0166-218x(01)00320-1.

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36

Na, Hyeon-Suk, Chung-Nim Lee, and Otfried Cheong. "Voronoi diagrams on the sphere." Computational Geometry 23, no. 2 (2002): 183–94. http://dx.doi.org/10.1016/s0925-7721(02)00077-9.

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37

Drezner, Tammy, and Zvi Drezner. "Voronoi diagrams with overlapping regions." OR Spectrum 35, no. 3 (2012): 543–61. http://dx.doi.org/10.1007/s00291-012-0292-5.

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38

Chew, L. P., and S. Fortune. "Sorting helps for voronoi diagrams." Algorithmica 18, no. 2 (1997): 217–28. http://dx.doi.org/10.1007/bf02526034.

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39

Shirriff, Ken. "Generating fractals from Voronoi diagrams." Computers & Graphics 17, no. 2 (1993): 165–67. http://dx.doi.org/10.1016/0097-8493(93)90100-n.

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40

Kühn, Ulrich. "Local calculation of Voronoi diagrams." Information Processing Letters 68, no. 6 (1998): 307–12. http://dx.doi.org/10.1016/s0020-0190(98)00180-x.

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41

Albers, Gerhard, Leonidas J. Guibas, Joseph S. B. Mitchell, and Thomas Roos. "Voronoi Diagrams of Moving Points." International Journal of Computational Geometry & Applications 08, no. 03 (1998): 365–79. http://dx.doi.org/10.1142/s0218195998000187.

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Consider a set of n points in d-dimensional Euclidean space, d ≥ 2, each of which is continuously moving along a given individual trajectory. As the points move, their Voronoi diagram changes continuously, but at certain critical instants in time, topological events occur that cause a change in the Voronoi diagram. In this paper, we present a method of maintaining the Voronoi diagram over time, at a cost of O( log n) per event, while showing that the number of topological events has an upper bound of O(ndλs(n)), where λs(n) is the (nearly linear) maximum length of a (n,s)-Davenport-Schinzel se

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42

Chou, J. J. "Voronoi diagrams for planar shapes." IEEE Computer Graphics and Applications 15, no. 2 (1995): 52–59. http://dx.doi.org/10.1109/38.365006.

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43

Canas, Guillermo D., and Steven J. Gortler. "Orphan-Free Anisotropic Voronoi Diagrams." Discrete & Computational Geometry 46, no. 3 (2011): 526–41. http://dx.doi.org/10.1007/s00454-011-9372-6.

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44

Roos, Thomas. "Voronoi diagrams over dynamic scenes." Discrete Applied Mathematics 43, no. 3 (1993): 243–59. http://dx.doi.org/10.1016/0166-218x(93)90115-5.

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45

Aurenhammer, F., R. L. S. Drysdale, and H. Krasser. "Farthest line segment Voronoi diagrams." Information Processing Letters 100, no. 6 (2006): 220–25. http://dx.doi.org/10.1016/j.ipl.2006.07.008.

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46

Zhou, Meng, Jianyu Li, Chang Wang, Jing Wang, and Li Wang. "Applications of Voronoi Diagrams in Multi-Robot Coverage: A Review." Journal of Marine Science and Engineering 12, no. 6 (2024): 1022. http://dx.doi.org/10.3390/jmse12061022.

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In recent decades, multi-robot region coverage has played an important role in the fields of environmental sensing, target searching, etc., and it has received widespread attention worldwide. Due to the effectiveness in segmenting nearest regions, Voronoi diagrams have been extensively used in recent years for multi-robot region coverage. This paper presents a survey of recent research works on region coverage methods within the framework of the Voronoi diagram, to offer a perspective for researchers in the multi-robot cooperation domain. First, some basic knowledge of the Voronoi diagram is i

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47

N. Musthafa, Haja-Sherief, and Jason Walker. "Design of Trabecular Bone Mimicking Voronoi Lattice-Based Scaffolds and CFD Modelling of Non-Newtonian Power Law Blood Flow Behaviour." Computation 12, no. 12 (2024): 241. https://doi.org/10.3390/computation12120241.

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Designing scaffolds similar to the structure of trabecular bone requires specialised algorithms. Existing scaffold designs for bone tissue engineering have repeated patterns that do not replicate the random stochastic porous structure of the internal architecture of bones. In this research, the Voronoi tessellation method is applied to create random porous biomimetic structures. A volume mesh created from the shape of a Zygoma fracture acts as a boundary for the generation of random seed points by point spacing to create Voronoi cells and Voronoi diagrams. The Voronoi lattices were obtained by

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48

Rezende, Flavio Astolpho Vieira Souto, Renan M. Varnier Almeida, and Flavio F. Nobre. "Diagramas de Voronoi para a definição de áreas de abrangência de hospitais públicos no Município do Rio de Janeiro." Cadernos de Saúde Pública 16, no. 2 (2000): 467–75. http://dx.doi.org/10.1590/s0102-311x2000000200017.

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No planejamento de recursos em saúde é importante o conhecimento da área de abrangência de uma unidade. Os Diagramas de Voronoi constituem uma técnica para tal; são polígonos construídos de tal forma que as bordas de polígonos adjacentes encontram-se eqüidistantes de seus respectivos pontos geradores. Uma modificação nas áreas de abrangência assim definidas é sua ponderação (Diagramas de Voronoi ponderados), representando a capacidade da unidade de forma mais real. No presente trabalho foram utilizados, como pontos geradores, 21 hospitais gerais públicos no Rio de Janeiro, RJ. Inicialmente for

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49

DJIDJEV, HRISTO N., and ANDRZEJ LINGAS. "ON COMPUTING VORONOI DIAGRAMS FOR SORTED POINT SETS." International Journal of Computational Geometry & Applications 05, no. 03 (1995): 327–37. http://dx.doi.org/10.1142/s0218195995000192.

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We show that the Voronoi diagram of a finite sequence of points in the plane which gives sorted order of the points with respect to two perpendicular directions can be computed in linear time. In contrast, we observe that the problem of computing the Voronoi diagram of a finite sequence of points in the plane which gives the sorted order of the points with respect to a single direction requires Ω(n log n) operations in the algebraic decision tree model. As a corollary from the first result, we show that the bounded Voronoi diagrams of simple n-vertex polygons which can be efficiently cut into

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50

Costello, B. P. J. de Lacy, I. Jahan, and A. Adamatzky. "Sequential Voronoi Diagram Calculations using Simple Chemical Reactions." International Journal of Nanotechnology and Molecular Computation 3, no. 3 (2011): 29–41. http://dx.doi.org/10.4018/ijnmc.2011070103.

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Abstract:

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 para

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