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Generalized Pythagoras Trees: A Fractal Approach to Hierarchy Visualization
[chapter]
2015
Communications in Computer and Information Science
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We hence extend Pythagoras Trees to arbitrarily branching trees by adapting the geometry of the original fractal approach. ...
Each vertex in the hierarchy is visualized as a rectangle sized according to a metric. ...
Acknowledgments We would like to thank Kay Nieselt, University of Tübingen, for providing the NCBI taxonomy dataset. ...
doi:10.1007/978-3-319-25117-2_8
fatcat:55jbif4z4be7vohlv6fwjqc75u
Pythagorean Triplets, Integral Apollonians and The Hofstadter Butterfly
[article]
2018
arXiv
pre-print
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The "butterfly fractal" describes a physical system of electrons in a crystal in a magnetic field, representing exotic states of matter known as integer quantum Hall states. ...
Here we show that these abstract objects are related with a quantum fractal made up of integers, known as the Hofstadter Butterfly. ...
However, it is asymptotically approached as one descends deeper and deeper into the hierarchies of the Apollonian. ...
arXiv:1802.04585v3
fatcat:c7hsvqc36jb27od72hfy5ljbyi
Unified approach to catastrophic events: from the normal state to geological or biological shock in terms of spectral fractal and nonlinear analysis
2006
Natural Hazards and Earth System Sciences
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The results suggest that a unified theory may exist for the ways in which firing neurons and opening cracks organize themselves to produce a large crisis, while the preparation of an epileptic shock or ...
A basic reason for our interest in complexity is the striking similarity in behavior close to irreversible phase transitions among systems that are otherwise quite different in nature. ...
We gratefully acknowledge financial support by the European Union program EPEAEK/PYTHAGORAS 70/3/7357. ...
doi:10.5194/nhess-6-205-2006
fatcat:tfmhzlc6l5gtvdulkytztuxdzi
Grain scale deformation in ultra-high-pressure metamorphic rocks—an indicator of rapid phase transformation
2005
Earth and Planetary Science Letters
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The results suggest that a unified theory may exist for the ways in which firing neurons and opening cracks organize themselves to produce a large crisis, while the preparation of an epileptic shock or ...
A basic reason for our interest in complexity is the striking similarity in behavior close to irreversible phase transitions among systems that are otherwise quite different in nature. ...
We gratefully acknowledge financial support by the European Union program EPEAEK/PYTHAGORAS 70/3/7357. ...
doi:10.1016/j.epsl.2004.10.012
fatcat:xahdmxpllna23bw2ykrlagc4l4
Integrating Various Neural Features Based on Mechanism of Intricate Balance and Ongoing Activity: Unified Neural Account Underlying and Correspondent to Mental Phenomena
2021
World Journal of Neuroscience
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from large number of interacting components from lower hierarchy. ...
In addition to experimental approach, computational simulation may complement our understanding of brain principles. ...
Some fractal objects are artificial, such as Koch snowflake, Sierpinski Triangle, Dragon curve, Pythagoras tree and Cantor set [80] . ...
doi:10.4236/wjns.2021.112014
fatcat:j2etoe7aznf7ddleuuidm6e4ma
A language-driven reverse-engineering tool for the analysis of architectural precedents: A Palladian case study
2021
Spatium
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The visual tool consists of four main layers: the morphological, the semantic, the semiotic, and the pragmatic. To test the tool? ...
s applicability, a prominent precedent from the Palladian designs is analyzed as a case study. ...
It also includes graphic representations such as the Nine-Square Grid (9SG), Pythagoras tree and the fractal chart of recurrent ratios. ...
doi:10.2298/spat2145021e
fatcat:gvedlheaqrc23mfxvuzhop4lei
Methods and Measures for Analyzing Complex Street Networks and Urban Form
[article]
2017
arXiv
pre-print
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It introduces a new tool, OSMnx, to collect street network and other urban form data for anywhere in the world, then analyze and visualize them. ...
Finally, it presents a large empirical study of 27,000 street networks, examining their metric and topological complexity relevant to urban design, transportation research, and the human experience of ...
Rather, each simply refers to the general directionality of a process in terms of the system's hierarchy. ...
arXiv:1708.00845v1
fatcat:aewkj6gl4ve3xm4iciufjgtc74
From Vecten's Theorem to Gamow's Problem: Building an Empirical Classification Model for Sequential Instructional Problems in Geometry
2019
Journal of Education and Practice
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Its contribution to our knowledge in the area of the didactics of mathematics lies in the fact that this sequence of problems is regarded as a process whereby students develop a sequentially deeper understanding ...
I shall introduce five types of geometrical problems applying the meaning of Linking Visual Active Representations (LVARs). ...
island, annotated in green and two dynamic fractal trees placed on the island. ...
doi:10.7176/jep/10-5-01
fatcat:g3lttulvdzgwjjhfmazl6ntwyu
Soil Image Segmentation and Texture Analysis: A Computer Vision Approach
2005
IEEE Geoscience and Remote Sensing Letters
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We examine a sophisticated integration of some modern methods from computer vision for image feature extraction, texture analysis, and segmentation into homogeneous regions, relevant to soil micromorphology ...
We also briefly demonstrate their applicability to remote sensing images. ...
The corresponding residuals constitute a hierarchy of multiscale texture components. ...
doi:10.1109/lgrs.2005.851752
fatcat:dzz2cvbtonfyho5d5rwjpnmmby
Methods and Measures for Analyzing Complex Street Networks and Urban Form
2017
Social Science Research Network
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Rather, each simply refers to the general directionality of a process in terms of the system's hierarchy. ...
Jacobs (1995) argues that buildings need multiple varied surfaces for light to move constantly over to generate visual complexity. ...
Chapter 5 introduced a new software tool, OSMnx, to download, analyze, and visualize street network and building footprint data from OpenStreetMap. ...
doi:10.2139/ssrn.3012684
fatcat:dgujgwk7argjdjvlgkjhbcp4tm
The 5th dimension of scalar space-time, its metric and superorganisms
2020
Zenodo
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To prove the scientific existence of a space-time dimension we need to find "a metric co-invariant function that relates its space-time parameters allowing to travel through it". (Klein). ...
smaller seed with faster time cycles, evolve as an organism emerging as a bigger ∆ºnetwork organism, to live within a larger ∆+1world of slower 'Deep time cycles', to die back dissolving its information ...
Wonder if I am the only one in this lost rock of the Universe ): Now regarding those drawings and our visualization of the interplay of S-flat›T-curved worldcycles‹ℜ-scales, as a general rule to visualize ...
doi:10.5281/zenodo.4318706
fatcat:2k5h5gbo5jgizieoappt32ai5a
Modeling Creativity: Case Studies in Python
[article]
2014
arXiv
pre-print
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Our aim is to construct computer models that exhibit creativity in an artistic context, that is, that are capable of generating or evaluating an artwork (visual or linguistic), an interesting new idea, ...
Modeling Creativity examines creativity in a number of different perspectives: from its origins in nature, which is essentially blind, to humans and machines, and from generating creative ideas to evaluating ...
Acknowledgements The authors of DrawBot, Just van Rossum and Erik van Blokland, define the simplicity of a computational approach to art and design in terms of volume, complexity and variation: ...
arXiv:1410.0281v1
fatcat:an7qvt47fbeqjgx5jmhrrnijsm
Consciousness and quantum mechanics of macroscopic systems
[article]
2016
arXiv
pre-print
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We suggest they are also common to biological physics and may describe how the brain works. ...
The latter has its evident counterparts in ancient Indian philosophy and provides a framework for unification of physical and mental phenomena. ...
Acknowledgements The author is thankful for hospitality to Växjö University (Sweden), where the draft of this paper have been prepared, and to Drs. A.Khrennikov and B.G.Sidharth for useful comments. ...
arXiv:1607.04400v2
fatcat:3hcl6pgmunannnqlqgmsyas22a
Marriages of mathematics and physics: A challenge for biology
2017
Progress in Biophysics and Molecular Biology
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b s t r a c t The human attempts to access, measure and organize physical phenomena have led to a manifold construction of mathematical and physical spaces. ...
In particular, the way the geometric and algebraic approaches organize knowledge is analyzed as a cross-disciplinary and cross-cultural issue and will be examined in Mathematical Physics and Biology. ...
That is, the linear element, which grounds the metric relations, does not need to be represented as the square root of a second order differential form (Pythagoras theorem), but more generally as ds 2 ...
doi:10.1016/j.pbiomolbio.2017.09.006
pmid:28887142
fatcat:y57fcxef4ja7nl5akks6ekn7om
Recent research on geometry education: an ICME-13 survey team report
2016
ZDM: Mathematics Education
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For example, children are asked to use tools to complete the outline of a symmetric tree that has been partially erased, but that is the dilation and rotation of another intact tree. ...
Further testing of this sort of approach would be valuable, as would further research on other aspects of the model of the five-phase approach to teaching geometry. ...
education of the future generation. ...
doi:10.1007/s11858-016-0796-6
fatcat:jbalhe5tj5calhfshjcauhzuby
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