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On the structure of self-similar sets

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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

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Geometry of Discrete Groups
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Über die stetige Abbildung einer Linie auf ein Flächenstück
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Sur une courbe, qui remplit toute une aire plane
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Zur Geometrie der Zahlen
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Ueber die stetige Abbildung einer Line auf ein Fl�chenst�ck
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Sur une courbe, qui remplit toute une aire plane
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On Jordan ARCS and Lipschitz classes of functions defined on them
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Composition of contractions
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Invariant sets under iteration of rational functions
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The differentiability of Pólya's function
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Peano curves and smoothness of functions
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Recurrent sets
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The Geometry of Fractal Sets
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The fractional dimensional theory of continued fractions
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Additive functions of intervals and Hausdorff measure
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On closest packing by equilateral triangles
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LINEAR SUPERPOSITIONS OF FUNCTIONS
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Analytic Topology
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On the functional equation 𝑓(𝑥+𝑦)=𝑓(𝑥)+𝑓(𝑦)
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On Certain Crinkly Curves
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A Jordan Curve of Positive Area
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On Some Singular Monotonic Functions Which Are Strictly Increasing
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Topologies on spaces of subsets
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The Fractal Geometry of Nature
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On the functional equation $\frac{1}{p}\{f(\frac{x}{p})+\cdots+f(\frac{x+p-1}{p})\}=\lambda f(\mu x)$
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Scrambled sets on compact metric spaces
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Dynamics of Caianiello’s equation
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A function not constant on a connected set of critical points
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Occurrence of apatite and associated gangue minerals in the Toyoha deposits, west Hokkaido, Japan.
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Ergodic Theory and Information
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Ergodic Theory and Information
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Ergodic Theory and Information.
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On Singular Fourier-Stieltjes Transforms
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On Symmetric Bernoulli Convolutions
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On a Family of Symmetric Bernoulli Convolutions
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The Fractal Geometry of Nature.
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On some properties of set-dynamical systems
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Sur la théorie de la mesure dans les espaces combinatoires et son application au calcul des probabilités. I. Variables indépendantes
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A continuous real-valued function on $E^n$ almost everywhere 1-1
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On the structure of self-similar fractals

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Topological Fractals Revisited
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Self‐Similar Sets 2. A Simple Approach to the Topological Structure of Fractals
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Effective Contraction Theorem and Its Application
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The Dynamics of Self-Similar Sets on S 2 and Complex Dynamics
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Uniqueness of Invariant Measures for Place-Dependent Random Iterations of Functions
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On Dendrites Generated by Symmetric Polygonal Systems: The Case of Regular Polygons
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Introduction
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Abstract Similarity, Fractals, and Chaos
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Transformations Between Fractals
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Substitutions, branching processes and fractal sets
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Interpolation fractale
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Topological aspects of self-similar sets and singular functions
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On $$\delta $$-deformations of Polygonal Dendrites
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Iterated function systems a rising from recursive estimation problems
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Hausdorff measure of infinitely generated self-similar sets
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Weyl's problem for the spectral distribution of Laplacians on P.C.F. self-similar fractals
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Self-similar sets from the topological point of view
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A generalization of Hata-Yamaguti’s results on the Takagi function II: Multinomial case
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Dynamical systems on dragon domains
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A harmonic calculus on the Sierpinski spaces
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Remarks on self-similarity
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On operators defining a family of nonanalyticC ∞-functions
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A Characterization of Self-similar Symbolic Spaces
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Some results for conjugate equations
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On the connectedness of self-affine attractors
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Contractive Iterated Function Systems Enriched with Nonexpansive Maps
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Ends of iterated function systems
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Fractal tiles and quasidisks
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Iterated Function Systems Enriched with Symmetry
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On a Theorem of Bandt and Wang and Its Extension to p2-tiles
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On Weakly Hyperbolic Iterated Function Systems
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On $$\mathbb {P}$$ P -Weakly Hyperbolic Iterated Function Systems
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Space-filling curves and geodesic laminations. II: Symmetries
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Radix expansions and connectedness of planar self-affine fractals
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A note on Hata’s tree-like sets
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On Hausdorff dimension of invariant measures arising from non-contractive iterated function systems
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Generalized Iterated Function Systems with Place Dependent Probabilities
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Arcwise connectedness of the boundary of connected self-similar sets
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A Survey on Topological Properties of Tiles Related to Number Systems
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Topology of crystallographic tiles
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Connectedness of planar self-affine sets associated with non-collinear digit sets
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Singularity Results for Functional Equations Driven by Linear Fractional Transformations
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On self-affine tiles that are homeomorphic to a ball
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On the connectivity of graph Lipscomb’s spaces
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Connectedness of invariant sets of graph-directed IFS
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Self-similarity of linear cellular automata
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Julia sets and self-similar sets
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Approximations of fractal sets
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Topological structure of fractal squares
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Zeros of {-1, 0, 1} Power Series and Connectedness Loci for Self-Affine Sets
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Power series and the open set condition of Hutchinson
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Julia sets of postcritically finite rational maps and topological self-similar sets
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Topology and separation of self-similar fractals in the plane
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Fractaln-gons and their Mandelbrot sets
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Space-filling curves of self-similar sets (I): iterated function systems with order structures
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Continuity of filled-in Julia sets and the closing lemma
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Multifractal analysis of non-uniformly contracting iterated function systems
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Space-filling curves of self-similar sets (II): edge-to-trail substitution rule
inferred← citeshttps://doi.org/10.1088/1361-6544/aba0c4openalex-snapshot
Topological Hausdorff dimension of fractal squares and its application to Lipschitz classification*
inferred← citeshttps://doi.org/10.1088/1361-6544/abd611openalex-snapshot
Fractal squares with finitely many connected components *
inferred← citeshttps://doi.org/10.1088/1361-6544/ac3c2copenalex-snapshot
Decay of correlations for weakly expanding dynamical systems with Dini potentials under optimal quasi-gap condition
inferred← citeshttps://doi.org/10.1088/1361-6544/acd21eopenalex-snapshot
Vector-valued Ruelle operator for weakly contractive IFS and Dini matrix potentials
inferred← citeshttps://doi.org/10.1088/1751-8113/45/46/463001openalex-snapshot
Laplace operators on fractals and related functional equations
inferred← citeshttps://doi.org/10.1090/ecgd/305openalex-snapshot
Iterated function system quasiarcs
inferred← citeshttps://doi.org/10.1090/proc/13182openalex-snapshot
On cut sets of attractors of iterated function systems
inferred← citeshttps://doi.org/10.1090/s0002-9939-04-07708-1openalex-snapshot
The OSC does not imply the SOSC for infinite iterated function systems
inferred← citeshttps://doi.org/10.1090/s0002-9939-08-09349-0openalex-snapshot
Self-similar sets with an open set condition and great variety of overlaps
inferred← citeshttps://doi.org/10.1090/s0002-9939-1992-1100644-3openalex-snapshot
Self-similar sets. VII. A characterization of self-similar fractals with positive Hausdorff measure
inferred← citeshttps://doi.org/10.1090/s0002-9939-1992-1132850-6openalex-snapshot
Attractors of Iterated Function Systems
inferred← citeshttps://doi.org/10.1090/s0002-9947-07-04106-2openalex-snapshot
Disklikeness of planar self-affine tiles
inferred← citeshttps://doi.org/10.1090/s0002-9947-1993-1076617-1openalex-snapshot
Harmonic Calculus on P.C.F. Self-Similar Sets
inferred← citeshttps://doi.org/10.1090/s0025-5718-09-02301-1openalex-snapshot
Disk-like tiles and self-affine curves with noncollinear digits
inferred← citeshttps://doi.org/10.1090/tran/7055openalex-snapshot
Topological properties of a class of self-affine tiles in $\mathbb {R}^3$
inferred← citeshttps://doi.org/10.1090/tran/7930openalex-snapshot
On self-affine tiles whose boundary is a sphere
inferred← citeshttps://doi.org/10.1109/icds47004.2019.8942348openalex-snapshot
IFSAM: A New Mathematical Technique for Additive Manufacturing based on Iterated Functions System
inferred← citeshttps://doi.org/10.1109/icmew.2016.7574722openalex-snapshot
Creating Celtic art using fractal image generation
inferred← citeshttps://doi.org/10.1117/12.696052openalex-snapshot
Fractal transformations of harmonic functions
inferred← citeshttps://doi.org/10.1134/s0037446614020128openalex-snapshot
The shark teeth is a topological IFS-attractor
inferred← citeshttps://doi.org/10.1134/s1055134425030010openalex-snapshot
On Self-Similar Dendrites with Intersecting Copies over Polygonal Trees
inferred← citeshttps://doi.org/10.1142/9789814343084_0007openalex-snapshot
SPIRAL-BASED SELF-SIMILAR SETS
inferred← citeshttps://doi.org/10.1142/s0218348x0200104xopenalex-snapshot
TOPOLOGICAL STRUCTURE OF SELF-SIMILAR SETS
inferred← citeshttps://doi.org/10.1142/s0218348x04002653openalex-snapshot
A TECHNIQUE IN THE TOPOLOGY OF CONNECTED SELF-SIMILAR TILES
inferred← citeshttps://doi.org/10.1142/s0218348x1000510xopenalex-snapshot
REMARKS ON SELF-AFFINE FRACTALS WITH POLYTOPE CONVEX HULLS
inferred← citeshttps://doi.org/10.1142/s0218348x16500080openalex-snapshot
ON THE CLASSIFICATION OF FRACTAL SQUARES
inferred← citeshttps://doi.org/10.1142/s0218348x17500219openalex-snapshot
WEAK SELF-SIMILAR SETS IN SEPARABLE COMPLETE METRIC SPACES
inferred← citeshttps://doi.org/10.1142/s0218348x17500530openalex-snapshot
CONNECTEDNESS OF SELF-AFFINE SETS WITH PRODUCT DIGIT SETS
inferred← citeshttps://doi.org/10.1142/s0218348x18500111openalex-snapshot
BASIC TOPOLOGICAL STRUCTURE OF FAST BASINS
inferred← citeshttps://doi.org/10.1142/s0218348x20500280openalex-snapshot
SPACE-FILLING CURVES OF SELF-SIMILAR SETS (III): SKELETONS
inferred← citeshttps://doi.org/10.1142/s0218348x22500918openalex-snapshot
FRACTAL NECKLACES WITH NO CUT POINTS
inferred← citeshttps://doi.org/10.1142/s0218348x99000220openalex-snapshot
DYNAMICAL SYSTEMS EXCITED BY TEMPORAL INPUTS: FRACTAL TRANSITION BETWEEN EXCITED ATTRACTORS
inferred← citeshttps://doi.org/10.1142/s021949370300067xopenalex-snapshot
Martin Metrics on the Sierpiński Gasket
inferred← citeshttps://doi.org/10.1145/3430279.3430290openalex-snapshot
A Novel Deterministic Chaos and Discrete Random Processes
inferred← citeshttps://doi.org/10.1145/378456.378502openalex-snapshot
Harnessing chaos for image synthesis
inferred← citeshttps://doi.org/10.1145/54852.378502openalex-snapshot
Harnessing chaos for image synthesis
inferred← citeshttps://doi.org/10.1155/2014/549741openalex-snapshot
Dimensions of Fractals Generated by Bi-Lipschitz Maps
inferred← citeshttps://doi.org/10.1215/kjm/1250283870openalex-snapshot
On the classification of self-similar sets determined by two contractions on the plane
inferred← citeshttps://doi.org/10.1215/kjm/1250517660openalex-snapshot
Distances on topological self-similar sets and the kneading determinants
inferred← citeshttps://doi.org/10.1215/kjm/1250520769openalex-snapshot
Some functional equations which generate both crinkly broken lines and curves
inferred← citeshttps://doi.org/10.1216/rmj-2019-49-1-307openalex-snapshot
Hartman-Grobman theorem for iterated function systems
inferred← citeshttps://doi.org/10.1216/rmjm/1181072539openalex-snapshot
Self-similarity
inferred← citeshttps://doi.org/10.12775/tmna.2015.076openalex-snapshot
Contractive function systems, their attractors and metrization
inferred← citeshttps://doi.org/10.12775/tmna.2018.049openalex-snapshot
Zero-dimensional compact metrizable spaces as attractors of generalized iterated function systems
inferred← citeshttps://doi.org/10.12775/tmna.2019.097openalex-snapshot
Sums of convex compacta as attractors of hyperbolic IFS's
inferred← citeshttps://doi.org/10.13189/ms.2018.060301openalex-snapshot
Hausdorff Measures and Hausdorff Dimensions of the Invariant Sets for Iterated Function Systems of Geometric Fractals
inferred← citeshttps://doi.org/10.14492/hokmj/1350911778openalex-snapshot
A generalization of Chaitin's halting probability $\Omega$ and halting self-similar sets
inferred← citeshttps://doi.org/10.1504/ijans.2013.052767openalex-snapshot
On the attractor of one-dimensional infinite iterated function systems
inferred← citeshttps://doi.org/10.1515/agms-2020-0125openalex-snapshot
Hölder Parameterization of Iterated Function Systems and a Self-Affine Phenomenon
inferred← citeshttps://doi.org/10.1515/anly-2014-1275openalex-snapshot
Restrictions of harmonic functions and Dirichlet eigenfunctions of the Hata set to the interval
inferred← citeshttps://doi.org/10.1515/integ.2009.022openalex-snapshot
A Planar Integral Self-Affine Tile with Cantor Set Intersections with Its Neighbors
inferred← citeshttps://doi.org/10.15507/2079-6900.25.202301openalex-snapshot
inferred← citeshttps://doi.org/10.15507/2079-6900.25.202301.519-530openalex-snapshot
On a class of self-affine sets on the plane given by six homotheties
inferred← citeshttps://doi.org/10.17762/atnaa.v7.i3.276openalex-snapshot
On the classification of fractal square dendrites
inferred← citeshttps://doi.org/10.21203/rs.3.rs-3967311/v1openalex-snapshot
Exploring Iterated Function Systems in Partial Metric Spaces: Theoretical Insights and Applications in Fractal Landscape Generation
inferred← citeshttps://doi.org/10.2206/kyushujm.50.541openalex-snapshot
ERGODICITY, UNIDIMENSIONALITY AND MULTIFRACTALITY OF SELF-SIMILAR MEASURES
inferred← citeshttps://doi.org/10.2298/fil2001153aopenalex-snapshot
Some topological structures of fractals and their related graphs
inferred← citeshttps://doi.org/10.24033/msmf.430openalex-snapshot
Topological properties of Rauzy fractals
inferred← citeshttps://doi.org/10.24193/fpt-ro.2017.1.16openalex-snapshot
About the attractors of infinite iterated function systems
inferred← citeshttps://doi.org/10.2478/auom-2014-0034openalex-snapshot
Arcwise connected attractors of infinite iterated function systems
inferred← citeshttps://doi.org/10.2478/s11533-012-0108-5openalex-snapshot
A class of continua that are not attractors of any IFS
inferred← citeshttps://doi.org/10.2478/s12175-008-0070-7openalex-snapshot
Fundamental group of tiles associated to quadratic canonical number systems
inferred← citeshttps://doi.org/10.2478/v10157-012-0044-5openalex-snapshot
Attractors of Infinite Iterated Function Systems Containing Con
inferred← citeshttps://doi.org/10.26493/2590-9770.1375.12aopenalex-snapshot
On deformation of polygonal dendrites preserving the intersection graph
inferred← citeshttps://doi.org/10.2969/aspm/02210231openalex-snapshot
Green Function on Self-Similar Trees
inferred← citeshttps://doi.org/10.2969/jmsj/04730381openalex-snapshot
Hausdorff dimensions of self-similar sets and shortest path metrics
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