Complex TreesBernat Espigulé

Historical presentation · 2019

A Family of Fern-like Ternary Complex Trees

Bernat Espigulé ·
Bridges 2019, Linz
24 slides · Recovered static slides

These static slides were recovered from the original Keynote export, in its original slide order. Animations, embedded video and incremental builds are not reproduced. Extracted text may omit mathematical notation visible in the images. Historical titles and notation are preserved.

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Slide 1: Bernat Espigulé www.ComplexTrees.com Mathematical Researcher at Universitat de Barcelona A Family of Fern-like Ternary Complex Trees
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Bernat Espigulé www.ComplexTrees.com Mathematical Researcher at Universitat de Barcelona A Family of Fern-like Ternary Complex Trees

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Slide 2: Bridges 2013 Wolfram Blog 2014 “Observant el Laberint Geomètric de la Natura”
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Bridges 2013 Wolfram Blog 2014 “Observant el Laberint Geomètric de la Natura”

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Slide 3: Geometric series Complex tree
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Geometric series Complex tree

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Slide 4: nodes empty string root complex-valued alphabet tip points complex tree letters word
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nodes empty string root complex-valued alphabet tip points complex tree letters word

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Slide 5: complex tree tipset complex tree
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complex tree tipset complex tree

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Slide 6: The tipset is a self-similar set First-level pieces
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The tipset is a self-similar set First-level pieces

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Slide 7: Key idea: “tip-to-tip gluing”
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Key idea: “tip-to-tip gluing”

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Slide 8: A Family of Fern-like Ternary Complex Trees
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A Family of Fern-like Ternary Complex Trees

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Slide 9: A Family of Fern-like Ternary Complex Trees
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A Family of Fern-like Ternary Complex Trees

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Slide 10: A Family of Fern-like Ternary Complex Trees
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A Family of Fern-like Ternary Complex Trees

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Slide 11: Thurston’s last paper Bill Thurston (1946 – 2012) ENTROPY IN DIMENSION ONE arxiv.org/abs/1402.2008
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Thurston’s last paper Bill Thurston (1946 – 2012) ENTROPY IN DIMENSION ONE arxiv.org/abs/1402.2008

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Slide 12: Bernat Espigulé bernat@espigule.com Mathematics is a process of staring hard enough at the fog of confusion to eventually break through to improved clarity. Thurston @ber
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Bernat Espigulé bernat@espigule.com Mathematics is a process of staring hard enough at the fog of confusion to eventually break through to improved clarity. Thurston @bernatree . #Bridges2019 #ComplexTrees Holomorphic Dynamics Group Núria Fagella Xavier Jarque

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Slide 13: Geodesics
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Geodesics

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Slide 14 — visual material from the original presentation

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Slide 15 — visual material from the original presentation

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Slide 16 — visual material from the original presentation

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Slide 17 — visual material from the original presentation

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Slide 18: Key idea: “tip-to-tip gluing”
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Key idea: “tip-to-tip gluing”

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Slide 19: Topological set
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Topological set

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Slide 20: Structurally stable tree Topological set
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Structurally stable tree Topological set

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Slide 21: A family of tipset connected trees
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A family of tipset connected trees

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Slide 22: A family of tipset connected trees
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A family of tipset connected trees

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Slide 23: All the branches of a tree at every stage of its height when put together are equal in thickness to the trunk. All the branches of a water [course] at every stage of its
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All the branches of a tree at every stage of its height when put together are equal in thickness to the trunk. All the branches of a water [course] at every stage of its course, if they are of equal rapidity, are equal to the body of the main stream. ⎯ Leonardo da Vinci 1452-1519

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Slide 24 — visual material from the original presentation

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