algorithmic mathematical art
play

Algorithmic Mathematical Art: Special Cases and Their Applications - PowerPoint PPT Presentation

Mar 13, 2023 •495 likes •1.21k views

DIMACS Workshop on Algorithmic Mathematical Art: Special Cases and Their Applications May 11 - 13, 2009 DIMACS Center, CoRE Building, Rutgers University Jean-Marie Dendoncker Dimacs Algorithmic Mathematical Art 1 DIMACS Algorithmic

  1. DIMACS Workshop on Algorithmic Mathematical Art: Special Cases and Their Applications May 11 - 13, 2009 DIMACS Center, CoRE Building, Rutgers University Jean-Marie Dendoncker Dimacs Algorithmic Mathematical Art 1

  2. DIMACS Algorithmic Mathematical Art May 11 - 13, 2009 J-M Dendoncker 1. Projects : IT’S MATHEMA G IC Van Maat tot Math - 0. A picture of the context A primary school with • 100% of the children who don’t speak Dutch at home • 65 % of the children are underprivileged • 45% are refugees “How can we help these children?” Dimacs Algorithmic Mathematical Art 2

  3. DIMACS Algorithmic Mathematical Art May 11 - 13, 2009 J-M Dendoncker 1. Projects : IT’S MATHEMA G IC Van Maat tot Math - 1.1 Arithmetic algorithm: tables of multiplication Dimacs Algorithmic Mathematical Art 3

  4. DIMACS Algorithmic Mathematical Art May 11 - 13, 2009 J-M Dendoncker 1. Projects : IT’S MATHEMA G IC Van Maat tot Math - 1.2 Geometric algortihm: wavefronts in a two dimensional representation Dimacs Algorithmic Mathematical Art 4

  5. DIMACS Algorithmic Mathematical Art May 11 - 13, 2009 J-M Dendoncker 1. Projects : IT’S MATHEMA G IC Van Maat tot Math - 1.2 Geometric algortihm: wavefronts in a two dimensional representation Dimacs Algorithmic Mathematical Art 5

  6. DIMACS Algorithmic Mathematical Art May 11 - 13, 2009 J-M Dendoncker 1. Projects : IT’S MATHEMA G IC Van Maat tot Math - 1.2 Geometric algortihm: wavefronts in a two dimensional representation Dimacs Algorithmic Mathematical Art 6

  7. DIMACS Algorithmic Mathematical Art May 11 - 13, 2009 J-M Dendoncker 1. Projects : IT’S MATHEMA G IC Van Maat tot Math - 1.2 Geometric algortihm: wavefronts in a two dimensional representation Dimacs Algorithmic Mathematical Art 7

  8. DIMACS Algorithmic Mathematical Art May 11 - 13, 2009 J-M Dendoncker 1. Projects : IT’S MATHEMA G IC Van Maat tot Math - 1.2 Geometric algortihm: wavefronts in a two dimensional representation Dimacs Algorithmic Mathematical Art 8

  9. DIMACS Algorithmic Mathematical Art May 11 - 13, 2009 J-M Dendoncker 1. Projects : IT’S MATHEMA G IC Van Maat tot Math - 1.2 Geometric algortihm: wavefronts in a two dimensional representation Dimacs Algorithmic Mathematical Art 9

  10. DIMACS Algorithmic Mathematical Art May 11 - 13, 2009 J-M Dendoncker 1. Projects : IT’S MATHEMA G IC Van Maat tot Math - 1.2 Geometric algortihm: wavefronts in a two dimensional representation Dimacs Algorithmic Mathematical Art 10

  11. DIMACS Algorithmic Mathematical Art May 11 - 13, 2009 J-M Dendoncker 1. Projects : IT’S MATHEMA G IC Van Maat tot Math - 1.2 Geometric algortihm: wavefronts in a two dimensional representation Dimacs Algorithmic Mathematical Art 11

  12. DIMACS Algorithmic Mathematical Art May 11 - 13, 2009 J-M Dendoncker 1. Projects : IT’S MATHEMA G IC Van Maat tot Math - 1.2 Geometric algortihm: wavefronts in a two dimensional representation Dimacs Algorithmic Mathematical Art 12

  13. DIMACS Algorithmic Mathematical Art May 11 - 13, 2009 J-M Dendoncker 1. Projects : IT’S MATHEMA G IC Van Maat tot Math - 1.2 Geometric algortihm: wavefronts in a two dimensional representation Dimacs Algorithmic Mathematical Art 13

  14. DIMACS Algorithmic Mathematical Art May 11 - 13, 2009 J-M Dendoncker 1. Projects : IT’S MATHEMA G IC Van Maat tot Math - 1.2 Geometric algortihm: wavefronts in a two dimensional representation Dimacs Algorithmic Mathematical Art 14

  15. DIMACS Algorithmic Mathematical Art May 11 - 13, 2009 J-M Dendoncker 1. Projects : IT’S MATHEMA G IC Van Maat tot Math - 1.2 Geometric algortihm: wavefronts in a two dimensional representation What if the basic curve is an ellipse instead of a circle? Dimacs Algorithmic Mathematical Art 15

  16. DIMACS Algorithmic Mathematical Art May 11 - 13, 2009 J-M Dendoncker 1. Projects : IT’S MATHEMA G IC Van Maat tot Math - 1.2 Geometric algortihm: wavefronts in a two dimensional representation Dimacs Algorithmic Mathematical Art 16

  17. DIMACS Algorithmic Mathematical Art May 11 - 13, 2009 J-M Dendoncker 1. Projects : IT’S MATHEMA G IC Van Maat tot Math - 1.2 Geometric algortihm: wavefronts in a two dimensional representation Dimacs Algorithmic Mathematical Art 17

  18. DIMACS Algorithmic Mathematical Art May 11 - 13, 2009 J-M Dendoncker 1. Projects : IT’S MATHEMA G IC Van Maat tot Math - 1.2 Geometric algortihm: wavefronts in a two dimensional representation Dimacs Algorithmic Mathematical Art 18

  19. DIMACS Algorithmic Mathematical Art May 11 - 13, 2009 J-M Dendoncker 1. Projects : IT’S MATHEMA G IC Van Maat tot Math - 1.2 Geometric algortihm: wavefronts in a two dimensional representation Dimacs Algorithmic Mathematical Art 19

  20. DIMACS Algorithmic Mathematical Art May 11 - 13, 2009 J-M Dendoncker 1. Projects : IT’S MATHEMA G IC Van Maat tot Math - 1.2 Geometric algortihm: wavefronts in a two dimensional representation Dimacs Algorithmic Mathematical Art 20

  21. DIMACS Algorithmic Mathematical Art May 11 - 13, 2009 J-M Dendoncker 1. Projects : IT’S MATHEMA G IC Van Maat tot Math - 1.2 Geometric algortihm: wavefronts in a two dimensional representation Dimacs Algorithmic Mathematical Art 21

  22. DIMACS Algorithmic Mathematical Art May 11 - 13, 2009 J-M Dendoncker 1. Projects : IT’S MATHEMA G IC Van Maat tot Math - 1.2 Geometric algortihm: wavefronts in a two dimensional representation Solution: Evolute ellipse Tetracuspid curve Dimacs Algorithmic Mathematical Art 22

  23. DIMACS Algorithmic Mathematical Art May 11 - 13, 2009 J-M Dendoncker 1. Projects : IT’S MATHEMA G IC Van Maat tot Math - 1.3 Geometric algortihm in a three dimensional representation A further generalization is to visualize curves in space 1.3.1 Wavefront surface 1.3.2 Cardioid and nephroid 1.3.3 Hyperbolic paraboloid 1.3.4 Conoid 1.3.5 Surface of Scherk 1.3.6 Elliptic surface Dimacs Algorithmic Mathematical Art 23

  24. DIMACS Algorithmic Mathematical Art May 11 - 13, 2009 J-M Dendoncker 1. Projects : IT’S MATHEMA G IC Van Maat tot Math - 1.3.1 Wavefronts in a three dimensional representation Dimacs Algorithmic Mathematical Art 24

  25. DIMACS Algorithmic Mathematical Art May 11 - 13, 2009 J-M Dendoncker 1. Projects : IT’S MATHEMA G IC Van Maat tot Math - 1.3.1 Wavefronts in a three dimensional representation Some properties of the wavefront surface Dimacs Algorithmic Mathematical Art 25

  26. elliptic ridge Point of curvature of the basic ellipse focal point of the basic ellipse Dimacs Algorithmic Mathematical Art 26

  27. DIMACS Algorithmic Mathematical Art May 11 - 13, 2009 J-M Dendoncker 1. Projects : IT’S MATHEMA G IC Van Maat tot Math - 1.3.2 Cardioid and nephroid in a three dimensional representation Dimacs Algorithmic Mathematical Art 27

  28. DIMACS Algorithmic Mathematical Art May 11 - 13, 2009 J-M Dendoncker 1. Projects : IT’S MATHEMA G IC Van Maat tot Math - 1.3.2 Cardioid and nephroid in a three dimensional representation Dimacs Algorithmic Mathematical Art 28

  29. DIMACS Algorithmic Mathematical Art May 11 - 13, 2009 J-M Dendoncker 1. Projects : IT’S MATHEMA G IC Van Maat tot Math - 1.3.3 Hyperbolic paraboloid Using the same way of curve stitching to visualise a parabola it’s possible to do the same in space. Dimacs Algorithmic Mathematical Art 29

  30. DIMACS Algorithmic Mathematical Art May 11 - 13, 2009 J-M Dendoncker 1. Projects : IT’S MATHEMA G IC Van Maat tot Math - 1.3.3 Hyperbolic paraboloid Dimacs Algorithmic Mathematical Art 30

  31. DIMACS Algorithmic Mathematical Art May 11 - 13, 2009 J-M Dendoncker 1. Projects : IT’S MATHEMA G IC Van Maat tot Math - 1.3.3 Hyperbolic paraboloid ?? I have a little problem: ‘ There’s a hole in my bucket ‘ by Harry Belafonte (and my mother) Dimacs Algorithmic Mathematical Art 31

  32. DIMACS Algorithmic Mathematical Art May 11 - 13, 2009 J-M Dendoncker 1. Projects : IT’S MATHEMA G IC Van Maat tot Math - 1.3.3 Hyperbolic paraboloid , NO Dimacs Algorithmic Mathematical Art 32

  33. DIMACS Algorithmic Mathematical Art May 11 - 13, 2009 J-M Dendoncker 1. Projects : IT’S MATHEMA G IC Van Maat tot Math - 1.3.4 Conoid Dimacs Algorithmic Mathematical Art 33

  34. DIMACS Algorithmic Mathematical Art May 11 - 13, 2009 J-M Dendoncker 1. Projects : IT’S MATHEMA G IC Van Maat tot Math - 1.3.5 Surface of Scherk The hyperbolic paraboloid should not be confused with the surface of Scherk (1798-1885). This surface is the only non trivial minimal translation surface. It can be given, with disregard of a translation and homothetic transformation, by the equation . cos y  z ln cos x It is formed by shifting in perpendicular planes without losing contact with each other the two curves , 1 1        g ( x ) ln cos( cx c 0 ) c h ( x ) ln cos( cx d 0 ) d 1 1 c c , , , with integration constants c c d d 0 1 0 1 Dimacs Algorithmic Mathematical Art 34

  35. DIMACS Algorithmic Mathematical Art May 11 - 13, 2009 J-M Dendoncker 1. Projects : IT’S MATHEMA G IC Van Maat tot Math - 1.3.5 Surface of Scherk as a translation surface as a minimal surface Dimacs Algorithmic Mathematical Art 35

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend

Towards Extensible Algorithmic Mathematical Knowledge Claudio Sacerdoti Coen

Towards Extensible Algorithmic Mathematical Knowledge Claudio Sacerdoti Coen

Towards Extensible Algorithmic Mathematical Knowledge Claudio Sacerdoti Coen <claudio.sacerdoticoen@unibo.it> Bialystok (PL), 26/07/16 Plan of the Talk Status of algorithmic knowledge in mathematical libraries and interactive

810 views • 49 slides
Mathematical Induction n The inductive proof will sometimes point out an algorithmic solution to a

Mathematical Induction n The inductive proof will sometimes point out an algorithmic solution to a

2/28/16 Why induction? n Prove algorithm correctness Mathematical Induction n The inductive proof will sometimes point out an algorithmic solution to a problem n Strongly connected to recursion Rosen Chapter 5 Motivation Motivation n A group

524 views • 8 slides
Mathematical Scientific Challenges of 5G Mrouane Debbah www.huawei.com Mathematical and

Mathematical Scientific Challenges of 5G Mrouane Debbah www.huawei.com Mathematical and

Security Level: Mathematical Scientific Challenges of 5G Mrouane Debbah www.huawei.com Mathematical and Algorithmic Sciences Lab HUAWEI TECHNOLOGIES CO., LTD. Outline Overview of 5G Part 1: Architecture Design of 5G: General

1.3k views • 103 slides
Some Algorithmic questions in Finite Group Theory V Arvind Institute of Mathematical Sciences,

Some Algorithmic questions in Finite Group Theory V Arvind Institute of Mathematical Sciences,

Some Algorithmic questions in Finite Group Theory V Arvind Institute of Mathematical Sciences, Chennai India email arvind@imsc.res.in June 30, 2015 Plan of Talk Permutation groups: background and some basic algorithms. Plan of Talk

1.62k views • 141 slides
Algorithmic Complexity Algorithmic Complexity "Algorithmic Complexity", also called

Algorithmic Complexity Algorithmic Complexity "Algorithmic Complexity", also called

Algorithmic Complexity Algorithmic Complexity "Algorithmic Complexity", also called "Running Time" or "Order of Growth", refers to the number of steps a program takes as a function of the size of its inputs. In

519 views • 28 slides
Algorithmic Geometry Background Computation of Weierstrass Placs for Function Fields

Algorithmic Geometry Background Computation of Weierstrass Placs for Function Fields

Algorithmics of Function Fields 3 Geometry Lecture 3 Weierstrass Places Mathematical Algorithmic Geometry Background Computation of Weierstrass Placs for Function Fields Isomorphisms and Automor- phisms Mathematical Background

424 views • 24 slides
Algorithmic Aspects of Example: How to . . . Algorithmic Aspects of . . . Analysis, Prediction,

Algorithmic Aspects of Example: How to . . . Algorithmic Aspects of . . . Analysis, Prediction,

Need for Analysis, . . . Symmetry: a . . . Algorithmic Aspects of . . . Algorithmic Aspects of Example: How to . . . Algorithmic Aspects of . . . Analysis, Prediction, and Example: Selecting . . . Control in Science and Acknowledgements

599 views • 44 slides
Decision Procedures An Algorithmic Point of View Deciding ILPs with Branch & Bound ILP

Decision Procedures An Algorithmic Point of View Deciding ILPs with Branch & Bound ILP

Decision Procedures An Algorithmic Point of View Deciding ILPs with Branch & Bound ILP References: Integer Programming / Laurence Wolsey Intro. To mathematical programming / Hillier, Lieberman Daniel Kroening and Ofer

315 views • 19 slides
Alternation as An Algorithmic Construct Moshe Y. Vardi Rice University Special Programme on

Alternation as An Algorithmic Construct Moshe Y. Vardi Rice University Special Programme on

Alternation as An Algorithmic Construct Moshe Y. Vardi Rice University Special Programme on Logic and Algorithms Newton Institute for Mathematical Sciences Complexity Theory Key CS Question , 1930s: What can be mechanized? Next Question ,

487 views • 34 slides
Decidable fragments of first order logic R. Ramanujam The Institute of Mathematical Sciences,

Decidable fragments of first order logic R. Ramanujam The Institute of Mathematical Sciences,

Decidable fragments of first order logic R. Ramanujam The Institute of Mathematical Sciences, Chennai, India jam@imsc.res.in Summary Modal logics have decent algorithmic properties, useful for specification and verification. Vardi,

460 views • 30 slides
Algorithmic Aspects of WQO (Well-Quasi-Ordering) Theory Part II: Algorithmic Applications of WQOs

Algorithmic Aspects of WQO (Well-Quasi-Ordering) Theory Part II: Algorithmic Applications of WQOs

Algorithmic Aspects of WQO (Well-Quasi-Ordering) Theory Part II: Algorithmic Applications of WQOs Sylvain Schmitz & Philippe Schnoebelen LSV, CNRS & ENS Cachan ESSLLI 2016, Bozen/Bolzano, Aug 22-26, 2016 Lecture notes & exercises

312 views • 30 slides
AI Ethics for AI Practitioners A design framework for building towards algorithmic justice Willie

AI Ethics for AI Practitioners A design framework for building towards algorithmic justice Willie

AI Ethics for AI Practitioners A design framework for building towards algorithmic justice Willie Costello The hazards of algorithmic systems Bias Discrimination Racism Sexism Surveillance The ideals of algorithmic systems Fairness

575 views • 28 slides
Spherical Tilings by Congruent Quadrangles Yohji Akama 1 Nico Van Cleemput 2 1 Mathematical

Spherical Tilings by Congruent Quadrangles Yohji Akama 1 Nico Van Cleemput 2 1 Mathematical

Spherical Tilings by Congruent Quadrangles Yohji Akama 1 Nico Van Cleemput 2 1 Mathematical Institute Graduate School of Science Tohoku University 2 Combinatorial Algorithms and Algorithmic Graph Theory Department of Applied Mathematics, Computer

1.24k views • 68 slides
Two Approaches To A Job Algorithmic: A task in which a set of established instructions are

Two Approaches To A Job Algorithmic: A task in which a set of established instructions are

Two Approaches To A Job Algorithmic: A task in which a set of established instructions are A NEW APPROACH TO MANAGEMENT AND followed to one conclusion. Extrinsic profit maximizes MOTIVATION Heuristic: Opposite of algorithmic,

176 views • 4 slides
Algorithmic Randomness Rod Downey Victoria University Wellington New Zealand Udine, 2018

Algorithmic Randomness Rod Downey Victoria University Wellington New Zealand Udine, 2018

Algorithmic Randomness Rod Downey Victoria University Wellington New Zealand Udine, 2018 Lets begin by examining the title: Algorithmic Randomness The idea is to use algorithmic means to ascribe meaning to the apparent

963 views • 50 slides
Treewidth reduction and algorithmic applications Treewidth reduction and algorithmic applications

Treewidth reduction and algorithmic applications Treewidth reduction and algorithmic applications

Content Treewdith Reduction Theorem The Algorithmic Motivation Proof Idea Concluding remarks Treewidth reduction and algorithmic applications Treewidth reduction and algorithmic applications Content Treewdith Reduction Theorem The

388 views • 34 slides
Detection and Estimation Theory Lecture 7 Mojtaba Soltanalian- UIC msol@uic.edu

Detection and Estimation Theory Lecture 7 Mojtaba Soltanalian- UIC msol@uic.edu

Detection and Estimation Theory Lecture 7 Mojtaba Soltanalian- UIC msol@uic.edu http://msol.people.uic.edu Based on ECE 531 Slides- 2011 (Prof. Natasha Devroye) Finding MVUE- what we discussed Finding MVUE- what we discussed Finding MVUE-

763 views • 17 slides
TEACH-BACK FOR EVERYONE YOU-TUBE IN YOUR OFFICE Patients remember less than Great for

TEACH-BACK FOR EVERYONE YOU-TUBE IN YOUR OFFICE Patients remember less than Great for

2/24/2017 A CLINICAL PEARL IS A distillation of clinical knowledge that is useful for solving every day medical problems It may be a tip, a way to remember something, a framing CLINICAL PEARLS of a problem FACULTY AND AUDIENCE May

272 views • 5 slides
Resonant absorption of dark matter in molecules Ken Van Tilburg (NYU & IAS) arXiv:1709.05354,

Resonant absorption of dark matter in molecules Ken Van Tilburg (NYU & IAS) arXiv:1709.05354,

Resonant absorption of dark matter in molecules Ken Van Tilburg (NYU & IAS) arXiv:1709.05354, Phys. Rev. X 8 , 041001 with Asimina Arvanitaki (Perimeter), Savas Dimopoulos (Stanford) Karl Berggren (MIT), Ilya Charaev (MIT), Jeff Chiles

616 views • 45 slides
ADA Coordinators: Roles & Responsibilities will begin at 2 pm ET Audio and Visual are

ADA Coordinators: Roles & Responsibilities will begin at 2 pm ET Audio and Visual are

ADA Coordinators: Roles & Responsibilities will begin at 2 pm ET Audio and Visual are provided through the on-line webinar system. This session is closed captioned. Individuals may also listen via telephone by dialing 1-857-232-0476 Access

296 views • 19 slides
MATH 8001 7 November 2014 Engaging students during lectures and discussions Turn in: your

MATH 8001 7 November 2014 Engaging students during lectures and discussions Turn in: your

MATH 8001 7 November 2014 Engaging students during lectures and discussions Turn in: your observation notes and the notes on your follow-up conversations. But first: check them if needed to remind yourself of one specific mathematical aspect

125 views • 8 slides
Heavy Quarks in Herwig 7 Simon Pltzer Particle Physics University of Vienna at the Heavy

Heavy Quarks in Herwig 7 Simon Pltzer Particle Physics University of Vienna at the Heavy

Heavy Quarks in Herwig 7 Simon Pltzer Particle Physics University of Vienna at the Heavy Flavour Hadronization Workshop CERN | 3 March 2020 Herwig 7 Overview [Herwig collaboration Eur.Phys.J. C76 (2016) 665] Two shower modules:

446 views • 13 slides
Sharing Experiments and their Provenance David Koop Juliana Freire Large-Scale Visualization and

Sharing Experiments and their Provenance David Koop Juliana Freire Large-Scale Visualization and

Sharing Experiments and their Provenance David Koop Juliana Freire Large-Scale Visualization and Data Analysis (VIDA) Center Polytechnic Institute of New York University www.vistrails.org NSF Community Codes 2012 Science Today 011100101

631 views • 47 slides
Discrete Structures Summer 2016 This Class Textbook Kenneth H. Rosen Discrete Mathematics and

Discrete Structures Summer 2016 This Class Textbook Kenneth H. Rosen Discrete Mathematics and

Discrete Structures Summer 2016 This Class Textbook Kenneth H. Rosen Discrete Mathematics and Its Applications , 7th edition, McGraw-Hill Also available as PDF (without DRM) Not necessary, but helpful 3 / 19 Course Requirements Homework

609 views • 24 slides

More recommend