Research of Pattern Formation

Overview

This collection brings together research and proceedings focused on pattern formation in natural and artificial systems. Edited by R. Takaki, it represents a comprehensive exploration of the mechanisms, mathematics, and applications of pattern formation across multiple disciplines.

Pattern formation—the spontaneous emergence of organized structures from seemingly random or uniform states—is a fundamental phenomenon in physics, biology, chemistry, and materials science. This collection examines both theoretical foundations and practical applications of pattern formation research.

Contents

Preliminary Material

• Prelims Download PDF (4.4 MB)
• Preface
  pp. v-vi
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• Contents
  pp. vii-x
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Chapter 1

• Introduction to Science of Pattern Formation
  R. Takaki | pp. 1-10
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Chapter 2: Geometry and Topology

• An Aspect of Katachi (Form)
  T. Ogawa | pp. 11-22
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• Generalization of Golden Ratio: Any Regular Polygon Contains Self-Similarity
  T. Ogawa | pp. 23-42
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• Projections of Four-Dimensional Regular Space Fillings
  K. Miyazaki and M. Shiozaki | pp. 43-53
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• Derivation of Some Equilateral Zonohedra and Star Zonohedra
  Y. Watanabe and T. Betsumiya | pp. 55-62
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• Topological Index and Some Counting Polynomials for Characterizing the Topological Structure and Properties of Molecular Graphs
  H. Hosoya | pp. 63-75
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• Map Fold a La Miura Style, Its Physical Characteristics and Application to the Space Science
  K. Miura | pp. 77-90
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• A Note on Intrinsic Geometry of Origami
  K. Miura | pp. 91-102
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Chapter 3: Crystal Growth

• Theoretical Study of Growth Patterns of Snow Crystals
  E. Yokoyama and T. Kuroda | pp. 103-110
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• Morphology and Formation Mechanism of Snow Polycrystals
  Y. Furukawa | pp. 111-119
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• Experimental Studies of Dendritic Ice Crystals Growing from the Vapor Phase
  T. Gonda | pp. 121-130
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• Monte Carlo Simulation and Single Nucleation Theory of Growth Shapes of a Crystal
  T. Ueta and Y. Saito | pp. 131-154
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• Mathematics of Crystal Growth
  Y. Shikata | pp. 155-162
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• Fractal Growth of Sodium Tartrate Crystals
  H. Ninomiya and S. Oki | pp. 163-167
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Chapter 4: Aggregation and Pattern Formation

• Experiments on Aggregations
  M. Matsushita | pp. 169-175
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• Hidden Singularities, Phase Transitions and Conservation Law in Multifractal Patterns
  K. Honda and M. Matsushita | pp. 177-195
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• Percolation Pattern in Continuous Media and Its Topology
  H. Tomita and C. Murakami | pp. 197-203
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• Various Growing Modes of Crystal in Diffusion Field
  H. Honjo | pp. 205-215
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• Diffusion-Limited Aggregation and Crystal Growth
  S. Ohta | pp. 217-238
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Chapter 5: Dynamic Patterns and Fluid Dynamics

• Formation and Transitions of Patterns in Thermal Convection
  O. Sano | pp. 265-288
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• The Motion of a Vortex Sheet in an Ideal Fluid
  Y. Kaneda | pp. 289-299
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• Chemically Driven Dynamic Patterns at an Oil-Water Interface: Experimental Analysis of Nonlinear Waves and Oscillations
  S. Kai, S. C. Müller, T. Mori, and M. Miki | pp. 301-327
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• Chemically Driven Dynamic Patterns at an Oil-Water Interface: Wave Form Analysis and Computer Simulation
  S. Kai, M. Miki, and T. Mori | pp. 329-341
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• Pattern Formations in Magnetically and Electrically Induced Freedericksz Transitions and in Multiplicative Stochastic Processes
  S. Kai, M. Imasaki, S. Yamaguchi, and F. Sagues | pp. 343-361
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• Self-Induced Vibration of an Evaporating Drop
  R. Takaki, N. Yoshiyasu, Y. Arai, and K. Adachi | pp. 363-375
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Chapter 6: Cellular Structures and Materials

• Mechanical Properties of Vertex Model for Two-Dimensional Random Cellular Structures
  K. Kawasaki, T. Okuzono, and T. Nagai | pp. 377-387
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• Dynamics of Cellular Pattern in Two Dimensions
  T. Nagai and K. Kawasaki | pp. 389-400
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• Elastic Instability of Gels upon Swelling
  K. Sekimoto and K. Kawasaki | pp. 401-409
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• Evolution of Antiphase Ordered Domain Structure and Phase Separation Activated by Ordering
  K. Shiiyama, H. Ninomiya, and T. Eguchi | pp. 411-430
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• Phase Transition, Spinodal Decomposition, and Pattern Formation in Polymer Gels
  S. Hirotsu | pp. 431-443
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Chapter 7: Geographic Patterns

• Selfsimilar Natures of Drainage Basins
  E. Tokunaga | pp. 445-468
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• Application of the Variation Principle to Geographic Pattern Analysis
  M. Hirano | pp. 469-483
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Chapter 8: Morphology and Biological Systems

• The Analysis of 3-D Organ Microstructure Assisted by Computers: Its Application to Histopathological Studies
  T. Takahashi, H. Yaegashi, T. Chiba, R. Chiba, and M. Suzuki | pp. 485-495
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• Cell Mosaic Patterns under the Direct Lateral Inhibition Rule of Differentiation
  H. Honda and M. Tanemura | pp. 497-505
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• Particle Number and Sizes Estimated from Sections – A History of Stereology
  K. Miyamoto | pp. 507-516
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• Stereology on Crack Geometry
  M. Oda | pp. 517-535
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Chapter 9: Image Processing and Visualization

• Role of Digital Image Processing in Morphology
  J. Toriwaki | pp. 537-548
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• The State of the Art of Medical 3-D Image Processing
  S. Yokoi and T. Yasuda | pp. 549-564
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• Image Analyzers: Its Development and New Application for 3-Dimentional Image Processing
  A. Kimura | pp. 565-570
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• 1/f Fluctuation in Japanese Brush Calligraphy
  S. Ozawa | pp. 571-579
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• A Study on Graphic Languages
  E. Izuhara | pp. 581-590
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About This Collection

The research presented here contributes to our understanding of fundamental biological processes, physical phenomena, and provides practical applications in materials design, biotechnology, and engineering.

Citation

Takaki, R. (Ed.). Research of Pattern Formation. KTK Scientific Publishers, Tokyo, 1994.

Related Publications

This collection complements other e-Library publications that explore morphology and form. For more on pattern formation in specific contexts, please see:

• Science on Form I: First International Symposium
• Science on Form II: Second International Symposium
• Pathology of Organ Structure – Pattern formation in biological systems
• Flow Visualization – Patterns in fluid dynamics