The Elementary Equation of the Conjugate Transformation for the Hexagonal Grid

Zheng, Zhijie; Maeder, Anthony

doi:10.1007/978-3-642-78114-8_2

Cited by 15 publications

(12 citation statements)

References 7 publications

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“…Since J. von Neumann initially proposed cellular automata [21] in the 1950s, much progress has been made in the fifty years of development 1,2) [22][23][24][25][26][27][28][29][30][31][32][33][34].…”

Section: Binary Function Spacesmentioning

confidence: 99%

A framework to express variant and invariant functional spaces for binary logic

Zheng

2010

Front. Electr. Electron. Eng. China

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A new framework has been developed to express variant and invariant properties of functions operating on a binary vector space. This framework allows for manipulation of dynamic logic using basic operations and permutations. Novel representations of binary functional spaces are presented. Current ideas of binary functional spaces are extended and additional conditions are added to describe new function representation schemes: F code and C code.Sizes of the proposed functional space representation schemes were determined. It was found that the complete representation for any set of functions operating on a binary sequence of numbers is larger than previously thought. The complete representation can only be described using a structure having a space of size 2 2 n Â 2 n ! for any given space of functions acting on a binary sequence of length n. The framework, along with the proposed coding schemes provides a foundational theory of variant and invariant logic in software and electricelectronic technology and engineering, and has uses in the analysis of the stability of rule-based, dynamic binary systems such as cellular automata.

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Section: Binary Function Spacesmentioning

confidence: 99%

A framework to express variant and invariant functional spaces for binary logic

Zheng

2010

Front. Electr. Electron. Eng. China

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“…Kunii & Takai (1989) applied a n-cell structure for analysis, classification and generation of visual objects using topology and homotopy tools in computer graphics (Kunii, Hioki & Shinagawa, 1993;Kunii & Kunii, 1999;Kunii & Shinagawa, 1992;Kunii & Takahashi, 1993;Kunii, Tsuchida, Arai, Matsuda, Shirahama & Miura, 1993). Zheng & Maeder (1992) proposed a balanced classification on binary images for conjugate classification and transformation of binary images on regular plan lattices in 1990s to visualise different configurations (Zheng, 1994;1996;Zheng & Leung, 1996;Zheng & Maeder, 1993). All such work used partial constructs of the Zheng & Zheng (2010) framework.…”

Section: Logic and Dynamic Systemsmentioning

confidence: 99%

A Framework of Variant Logic Construction for Cellular Automata

Zheng¹,

Zheng²,

Kunii³

2011

Cellular Automata - Innovative Modelling for Science and Engineering

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“…Following this scheme, quantitative measurements of feature indexing are investigated. Using the conjugate classification, it is always feasible to decompose a binary image into 2n feature [4] ( n images representing 0 feature points and . another n images representing 1 feature points).…”

Section: A New Schemementioning

confidence: 99%

“…The conjugate classification of the kernel form of the hexagonal grid is established by Zheng and Maeder [3] and further systematic investigations are shown in Zheng [4,5]. For a convenient description, the classification can be briefly described as follows.…”

Section: Conjugate Classification Of Kernel Formmentioning

confidence: 99%