Fractal curves

Hilbert curve

The Hilbert curve (also known as the Hilbert space-filling curve) is a continuous fractal space-filling curve first described by the German mathematician David Hilbert in 1891, as a variant of the space-filling Peano curves discovered by Giuseppe Peano in 1890. Because it is space-filling, its Hausdorff dimension is 2 (precisely, its image is the unit square, whose dimension is 2 in any definition of dimension; its graph is a compact set homeomorphic to the closed unit interval, with Hausdorff dimension 2). The Hilbert curve is constructed as a limit of piecewise linear curves. The length of the th curve is , i.e., the length grows exponentially with , even though each curve is contained in a square with area . (Wikipedia).

Hilbert curve
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Hilbert Curve

This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/2toQ.

From playlist 3D printing

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Developing Hilbert curve

This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/8pkP

From playlist 3D printing

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Anthony Licata: Hilbert Schemes Lecture 7

SMRI Seminar Series: 'Hilbert Schemes' Lecture 7 Kleinian singularities 2 Anthony Licata (Australian National University) This series of lectures aims to present parts of Nakajima’s book `Lectures on Hilbert schemes of points on surfaces’ in a way that is accessible to PhD students inter

From playlist SMRI Course: Hilbert Schemes

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More identities involving the Riemann-Zeta function!

By applying some combinatorial tricks to an identity from https://youtu.be/2W2Ghi9idxM we are able to derive two identities involving the Riemann-Zeta function. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist The Riemann Zeta Function

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Joshua Ciappara: Hilbert Schemes Lecture 10

SMRI Seminar Series: 'Hilbert Schemes' Lecture 10 Representations of Heisenberg algebras on homology of Hilbert schemes Joshua Ciappara (University of Sydney) This series of lectures aims to present parts of Nakajima’s book `Lectures on Hilbert schemes of points on surfaces’ in a way tha

From playlist SMRI Course: Hilbert Schemes

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Emily Cliff: Hilbert Schemes Lecture 3

SMRI Seminar Series: 'Hilbert Schemes' Lecture 3 The universal family on H Emily Cliff (University of Sydney) This series of lectures aims to present parts of Nakajima’s book `Lectures on Hilbert schemes of points on surfaces’ in a way that is accessible to PhD students interested in rep

From playlist SMRI Course: Hilbert Schemes

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Emily Cliff: Hilbert Schemes Lecture 6

SMRI Seminar Series: 'Hilbert Schemes' Lecture 6 GIT stability, quiver representations, & Hilbert schemes Emily Cliff (University of Sydney) This series of lectures aims to present parts of Nakajima’s book `Lectures on Hilbert schemes of points on surfaces’ in a way that is accessible to

From playlist SMRI Course: Hilbert Schemes

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Space-Filling Curves (2 of 4: Hilbert Curve)

More resources available at www.misterwootube.com

From playlist Exploring Mathematics: Fractals

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Some identities involving the Riemann-Zeta function.

After introducing the Riemann-Zeta function we derive a generating function for its values at positive even integers. This generating function is used to prove two sum identities. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist The Riemann Zeta Function

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Coding in the Cabana 3: Hilbert Curve

It's the third episode of Coding in the Cabana! On this snowy day, I attempt to animate the path of the classic "space filling curve" known as the Hilbert Curve. 💻https://thecodingtrain.com/CodingInTheCabana/003-hilbert-curve.html 🔗Hilbert Curve on Wikipedia: https://en.wikipedia.org/wik

From playlist Coding in the Cabana

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Hilbert's Curve: Is infinite math useful?

Space-filling curves, and the connection between infinite and finite math. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Home page: https://www.3blue1brown.com Supplement with more space-filling cu

From playlist Explainers

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Geometry and Topology in Quantum Mechanics - Mathematical Properties by N. Mukunda

DISCUSSION MEETING GEOMETRIC PHASES IN OPTICS AND TOPOLOGICAL MATTER ORGANIZERS: Subhro Bhattacharjee, Joseph Samuel and Supurna Sinha DATE: 21 January 2020 to 24 January 2020 VENUE: Madhava Lecture Hall, ICTS, Bangalore This is a joint ICTS-RRI Discussion Meeting on the geometric pha

From playlist Geometric Phases in Optics and Topological Matter 2020

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Ekaterina Amerik: Rational curves and contraction loci on holomorphic symplectic manifolds

VIRTUAL LECTURE RECORDED DURING SOCIAL DISTANCING Recording during the meeting "Varieties with Trivial Canonical Class " the April 06, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by

From playlist Virtual Conference

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The cohomology groups...Jacobians of planar curves - Luca Migliorini

Luca Migliorini University of Bologna; Member, School of Mathematics February 18, 2015 I will first discuss a relation between the cohomology groups (with rational coefficients) of the compactified Jacobian and those of the Hilbert schemes of a projective irreducible curve CC with planar

From playlist Mathematics

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Richard Thomas - Vafa-Witten Invariants of Projective Surfaces 4/5

This course has 4 sections split over 5 lectures. The first section will be the longest, and hopefully useful for the other courses. 1. Sheaves, moduli and virtual cycles 2. Vafa-Witten invariants: stable and semistable cases 3. Techniques for calculation --- virtual degeneracy loci, c

From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory

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The computational theory of Riemann–Hilbert problems (Lecture 1) by Thomas Trogdon

ORGANIZERS : Alexander Abanov, Rukmini Dey, Fabian Essler, Manas Kulkarni, Joel Moore, Vishal Vasan and Paul Wiegmann DATE & TIME : 16 July 2018 to 10 August 2018 VENUE : Ramanujan Lecture Hall, ICTS Bangalore This program aims to address various aspects of integrability and its role in

From playlist Integrable​ ​systems​ ​in​ ​Mathematics,​ ​Condensed​ ​Matter​ ​and​ ​Statistical​ ​Physics

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Cannon-Thurston maps: naturally occurring space-filling curves

Saul Schleimer and I attempt to explain what a Cannon-Thurston map is. Thanks to my brother Will Segerman for making the carvings, and to Daniel Piker for making the figure-eight knot animations. I made the animation of the (super crinkly) surface using our app (with Dave Bachman) for coh

From playlist GPU shaders

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Geometry of Teichmüller curves – Martin Möller – ICM2018

Dynamical Systems and Ordinary Differential Equations Invited Lecture 9.4 Geometry of Teichmüller curves Martin Möller Abstract: The study of polygonal billiard tables with simple dynamics led to a remarkable class of special subvarieties in the moduli of space of curves called Teichmüll

From playlist Dynamical Systems and ODE

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Anthony Henderson: Hilbert Schemes Lecture 4

SMRI Seminar Series: 'Hilbert Schemes' Lecture 4 Kleinian singularities 1 Anthony Henderson (University of Sydney) This series of lectures aims to present parts of Nakajima’s book `Lectures on Hilbert schemes of points on surfaces’ in a way that is accessible to PhD students interested i

From playlist SMRI Course: Hilbert Schemes

Related pages

Gray code | Locality-sensitive hashing | Rewriting | Giuseppe Peano | Hausdorff dimension | Hilbert R-tree | David Hilbert | Moore curve | Peano curve | List of fractals by Hausdorff dimension | Sierpiński curve | L-system | Fractal curve | Hilbert curve scheduling | Space-filling curve | R-tree