scholarly journals The Fractal Geometry of the Nymphalid Groundplan: Self-Similar Configuration of Color Pattern Symmetry Systems in Butterfly Wings

Insects ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 39
Author(s):  
Joji M. Otaki
Keyword(s):  
Symmetry Breaking ◽  
Fractal Geometry ◽  
Color Pattern ◽  
Central Symmetry ◽  
Color Patterns ◽  
Self Similarity ◽  
Developmental Potential ◽  
Butterfly Wings ◽  
Species Comparisons ◽  
Self Similar

The nymphalid groundplan is an archetypical color pattern of nymphalid butterflies involving three major symmetry systems and a discal symmetry system, which share the basic morphogenesis unit. Here, the morphological and spatial relationships among these symmetry systems were studied based on cross-species comparisons of nymphalid hindwings. Based on findings in Neope and Symbrenthia, all three major symmetry systems can be expressed as bands, spots, or eyespot-like structures, suggesting equivalence (homology) of these systems in developmental potential. The discal symmetry system can also be expressed as various structures. The discal symmetry system is circularly surrounded by the central symmetry system, which may then be surrounded by the border and basal symmetry systems, based mainly on findings in Agrias, indicating a unified supersymmetry system covering the entire wing. The border symmetry system can occupy the central part of the wing when the central symmetry system is compromised, as seen in Callicore. These results suggest that butterfly color patterns are hierarchically constructed in a self-similar fashion, as the fractal geometry of the nymphalid groundplan. This self-similarity is likely mediated by the serial induction of organizers, and symmetry breaking of the system morphology may be generated by the collision of opposing signals during development.

scholarly journals Long-Range Effects of Wing Physical Damage and Distortion on Eyespot Color Patterns in the Hindwing of the Blue Pansy Butterfly Junonia orithya

Insects ◽  
2018 ◽  
Vol 9 (4) ◽  
pp. 195 ◽  
Author(s):  
Joji Otaki
Keyword(s):  
Long Range ◽  
Color Pattern ◽  
Color Patterns ◽  
Physical Damage ◽  
Damage Site ◽  
Disk Size ◽  
Close Proximity ◽  
Butterfly Wings ◽  
Pattern Determination ◽  
Background Area

Butterfly eyespot color patterns have been studied using several different approaches, including applications of physical damage to the forewing. Here, damage and distortion experiments were performed, focusing on the hindwing eyespots of the blue pansy butterfly Junonia orithya. Physical puncture damage with a needle at the center of the eyespot reduced the eyespot size. Damage at the eyespot outer rings not only deformed the entire eyespot, but also diminished the eyespot core disk size, despite the distance from the damage site to the core disk. When damage was inflicted near the eyespot, the eyespot was drawn toward the damage site. The induction of an ectopic eyespot-like structure and its fusion with the innate eyespots were observed when damage was inflicted in the background area. When a small stainless ball was placed in close proximity to the eyespot using the forewing-lift method, the eyespot deformed toward the ball. Taken together, physical damage and distortion elicited long-range inhibitory, drawing (attracting), and inducing effects, suggesting that the innate and induced morphogenic signals travel long distances and interact with each other. These results are consistent with the distortion hypothesis, positing that physical distortions of wing tissue contribute to color pattern determination in butterfly wings.

Similarity Hashing: A Computer Vision Solution to the Inverse Problem of Linear Fractals

Fractals ◽  
1997 ◽  
Vol 05 (supp01) ◽  
pp. 39-50 ◽  
Author(s):  
John C. Hart ◽  
Wayne O. Cochran ◽  
Patrick J. Flynn
Keyword(s):  
Computer Vision ◽  
Inverse Problem ◽  
Heuristic Search ◽  
Fractal Geometry ◽  
Self Similarity ◽  
Geometric Hashing ◽  
Numerical Minimization ◽  
Self Similar ◽  
Vision Algorithm ◽  
Fractal Representation

The difficult task of finding a fractal representation of an input shape is called the inverse, problem of fractal geometry. Previous attempts at solving this problem have applied techniques from numerical minimization, heuristic search and image compression. The most appropriate domain from which to attack this problem is not numerical analysis nor signal processing, but model-based computer vision. Self-similar objects cause an existing computer vision algorithm called geometric hashing to malfunction. Similarity hashing capitalizes on this observation to not only detect a shape's morphological self-similarity but also find the parameters of its self-transformations.

Measures with uniform scaling scenery

2010 ◽  
Vol 31 (1) ◽  
pp. 33-48 ◽  
Author(s):  
MATAN GAVISH
Keyword(s):  
Time Series ◽  
Fractal Geometry ◽  
Empirical Distribution ◽  
Iterated Function Systems ◽  
Occupation Measure ◽  
Self Similarity ◽  
Almost Everywhere ◽  
Iterated Function ◽  
Self Similar ◽  
Uniform Scaling

AbstractWe introduce a property of measures on Euclidean space, termed ‘uniform scaling scenery’. For these measures, the empirical distribution of the measure-valued time series, obtained by rescaling around a point, is (almost everywhere) independent of the point. This property is related to existing notions of self-similarity: it is satisfied by the occupation measure of a typical Brownian motion (which is ‘statistically’ self-similar), as well as by the measures associated to attractors of affine iterated function systems (which are ‘exactly’ self-similar). It is possible that different notions of self-similarity are unified under this property. The proofs trace a connection between uniform scaling scenery and Furstenberg’s ‘CP processes’, a class of natural, discrete-time, measure-valued Markov processes, useful in fractal geometry.

Functional significance of preserved color patterns of mollusks from the Gosport Sand (Eocene) of Alabama

1988 ◽  
Vol 62 (01) ◽  
pp. 83-87 ◽  
Author(s):  
Patricia H. Kelley ◽  
Charles T. Swann
Keyword(s):  
Functional Morphology ◽  
Functional Significance ◽  
Intraspecific Variability ◽  
Color Pattern ◽  
Color Patterns ◽  
Historical Factors ◽  
Life Mode ◽  
Molluscan Fauna ◽  
Excellent Preservation ◽  
Architectural Constraints

The excellent preservation of the molluscan fauna from the Gosport Sand (Eocene) at Little Stave Creek, Alabama, has made it possible to describe the preserved color patterns of 15 species. In this study the functional significance of these color patterns is tested in the context of the current adaptationist controversy. The pigment of the color pattern is thought to be a result of metabolic waste disposal. Therefore, the presence of the pigment is functional, although the patterns formed by the pigment may or may not have been adaptive. In this investigation the criteria proposed by Seilacher (1972) for testing the functionality of color patterns were applied to the Gosport fauna and the results compared with life mode as interpreted from knowledge of extant relatives and functional morphology. Using Seilacher's criteria of little ontogenetic and intraspecific variability, the color patterns appear to have been functional. However, the functional morphology studies indicate an infaunal life mode which would preclude functional color patterns. Particular color patterns are instead interpreted to be the result of historical factors, such as multiple adaptive peaks or random fixation of alleles, or of architectural constraints including possibly pleiotropy or allometry. The low variability of color patterns, which was noted within species and genera, suggests that color patterns may also serve a useful taxonomic purpose.

scholarly journals Onset of the Mach Reflection of Zel’dovich–von Neumann–Döring Detonations

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 314
Author(s):  
Tianyu Jing ◽  
Huilan Ren ◽  
Jian Li
Keyword(s):  
Hot Spot ◽  
Mach Reflection ◽  
Near Field ◽  
The Self ◽  
Small Scale ◽  
Mach Stem ◽  
Self Similarity ◽  
Von Neumann ◽  
Similarity Problem ◽  
Self Similar

The present study investigates the similarity problem associated with the onset of the Mach reflection of Zel’dovich–von Neumann–Döring (ZND) detonations in the near field. The results reveal that the self-similarity in the frozen-limit regime is strictly valid only within a small scale, i.e., of the order of the induction length. The Mach reflection becomes non-self-similar during the transition of the Mach stem from “frozen” to “reactive” by coupling with the reaction zone. The triple-point trajectory first rises from the self-similar result due to compressive waves generated by the “hot spot”, and then decays after establishment of the reactive Mach stem. It is also found, by removing the restriction, that the frozen limit can be extended to a much larger distance than expected. The obtained results elucidate the physical origin of the onset of Mach reflection with chemical reactions, which has previously been observed in both experiments and numerical simulations.

scholarly journals Depressurization-Induced Nucleation in the “Polylactide-Carbon Dioxide” System: Self-Similarity of the Bubble Embryos Expansion

Polymers ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1115
Author(s):  
Dmitry Zimnyakov ◽  
Marina Alonova ◽  
Ekaterina Ushakova
Keyword(s):  
Initial Rate ◽  
Initial Pressure ◽  
External Pressure ◽  
Self Similarity ◽  
Embryo Formation ◽  
Linear Behavior ◽  
Joint Influence ◽  
External Pressures ◽  
Adiabatic Cooling ◽  
Self Similar

Self-similar expansion of bubble embryos in a plasticized polymer under quasi-isothermal depressurization is examined using the experimental data on expansion rates of embryos in the CO2-plasticized d,l-polylactide and modeling the results. The CO2 initial pressure varied from 5 to 14 MPa, and the depressurization rate was 5 × 10−3 MPa/s. The constant temperature in experiments was in a range from 310 to 338 K. The initial rate of embryos expansion varied from ≈0.1 to ≈10 µm/s, with a decrease in the current external pressure. While modeling, a non-linear behavior of CO2 isotherms near the critical point was taken into account. The modeled data agree satisfactorily with the experimental results. The effect of a remarkable increase in the expansion rate at a decreasing external pressure is interpreted in terms of competing effects, including a decrease in the internal pressure, an increase in the polymer viscosity, and an increase in the embryo radius at the time of embryo formation. The vanishing probability of finding the steadily expanding embryos for external pressures around the CO2 critical pressure is interpreted in terms of a joint influence of the quasi-adiabatic cooling and high compressibility of CO2 in the embryos.

scholarly journals Self-similar resistive circuits as fractal-like structures

2017 ◽  
Vol 40 (1) ◽  
Author(s):  
Claudio Xavier Mendes dos Santos ◽  
Carlos Molina Mendes ◽  
Marcelo Ventura Freire
Keyword(s):  
Scale Invariance ◽  
Self Similarity ◽  
General Properties ◽  
Modern Physics ◽  
Resistive Networks ◽  
Self Similar ◽  
And Mathematics ◽  
Definition Of ◽  
The Individual

Fractals play a central role in several areas of modern physics and mathematics. In the present work we explore resistive circuits where the individual resistors are arranged in fractal-like patterns. These circuits have some of the characteristics typically found in geometric fractals, namely self-similarity and scale invariance. Considering resistive circuits as graphs, we propose a definition of self-similar circuits which mimics a self-similar fractal. General properties of the resistive circuits generated by this approach are investigated, and interesting examples are commented in detail. Specifically, we consider self-similar resistive series, tree-like resistive networks and Sierpinski’s configurations with resistors.

TUBE FORMULAS FOR GRAPH-DIRECTED FRACTALS

Fractals ◽  
2010 ◽  
Vol 18 (03) ◽  
pp. 349-361 ◽  
Author(s):  
BÜNYAMIN DEMÍR ◽  
ALI DENÍZ ◽  
ŞAHIN KOÇAK ◽  
A. ERSIN ÜREYEN
Keyword(s):  
The Self ◽  
Self Similarity ◽  
Complex Dimensions ◽  
Tubular Neighborhoods ◽  
Self Similar ◽  
Tube Formulas

Lapidus and Pearse proved recently an interesting formula about the volume of tubular neighborhoods of fractal sprays, including the self-similar fractals. We consider the graph-directed fractals in the sense of graph self-similarity of Mauldin-Williams within this framework of Lapidus-Pearse. Extending the notion of complex dimensions to the graph-directed fractals we compute the volumes of tubular neighborhoods of their associated tilings and give a simplified and pointwise proof of a version of Lapidus-Pearse formula, which can be applied to both self-similar and graph-directed fractals.

scholarly journals On the scaling of shear-driven entrainment: a DNS study

2013 ◽  
Vol 732 ◽  
pp. 150-165 ◽  
Author(s):  
Harm J. J. Jonker ◽  
Maarten van Reeuwijk ◽  
Peter P. Sullivan ◽  
Edward G. Patton
Keyword(s):  
Reynolds Number ◽  
Lower Boundary ◽  
Square Root ◽  
Simulation Design ◽  
Self Similarity ◽  
Original Experiment ◽  
Turbulent Layer ◽  
Entrainment Velocity ◽  
Constant Shear Stress ◽  
Self Similar

AbstractThe deepening of a shear-driven turbulent layer penetrating into a stably stratified quiescent layer is studied using direct numerical simulation (DNS). The simulation design mimics the classical laboratory experiments by Kato & Phillips (J. Fluid Mech., vol. 37, 1969, pp. 643–655) in that it starts with linear stratification and applies a constant shear stress at the lower boundary, but avoids sidewall and rotation effects inherent in the original experiment. It is found that the layers universally deepen as a function of the square root of time, independent of the initial stratification and the Reynolds number of the simulations, provided that the Reynolds number is large enough. Consistent with this finding, the dimensionless entrainment velocity varies with the bulk Richardson number as$R{i}^{- 1/ 2} $. In addition, it is observed that all cases evolve in a self-similar fashion. A self-similarity analysis of the conservation equations shows that only a square root growth law is consistent with self-similar behaviour.

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