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Generalized Pythagoras Trees: A Fractal Approach to Hierarchy Visualization [chapter]

Fabian Beck, Michael Burch, Tanja Munz, Lorenzo Di Silvestro, Daniel Weiskopf
2015 Communications in Computer and Information Science  
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]

Indubala Satija
2018 arXiv   pre-print
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

K. A. Eftaxias, P. G. Kapiris, G. T. Balasis, A. Peratzakis, K. Karamanos, J. Kopanas, G. Antonopoulos, K. D. Nomicos
2006 Natural Hazards and Earth System Sciences  
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

Annette Lenze, Bernhard Stöckhert, Richard Wirth
2005 Earth and Planetary Science Letters  
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

Tien-Wen Lee, Gerald Tramontano
2021 World Journal of Neuroscience  
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

Buthayna Eilouti
2021 Spatium  
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]

Geoff Boeing
2017 arXiv   pre-print
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  
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

A. Sofou, G. Evangelopoulos, P. Maragos
2005 IEEE Geoscience and Remote Sensing Letters  
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

Geoff Boeing
2017 Social Science Research Network  
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

Luis Soto
2020 Zenodo  
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]

Tom De Smedt
2014 arXiv   pre-print
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]

M.V.Altaisky
2016 arXiv   pre-print
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

Arezoo Islami, Giuseppe Longo
2017 Progress in Biophysics and Molecular Biology  
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

Nathalie Sinclair, Maria G. Bartolini Bussi, Michael de Villiers, Keith Jones, Ulrich Kortenkamp, Allen Leung, Kay Owens
2016 ZDM: Mathematics Education  
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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