{
  "schema": "complex-trees/recovered-slides/2",
  "title": "Unfolding Complex Trees with n-fold rotational symmetry",
  "date": "2019-10-22",
  "event": "Illustrating Mathematics, ICERM",
  "author": "Bernat Espigulé",
  "format": "Recovered static slides",
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      "text": "Unfolding Complex Trees with\nn-fold rotational symmetry\nBernat Espigulé\nbernat@espigule.com\nXavier Jarque & Núria Fagella\nIllustrating Mathematics, ICERM, Brown University, October 2019\nwww.ComplexTrees.com",
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      "text": "\\\"Sur une courbe continue sans tangente, obtenue par une construction géométrique élémentaire.\\\"\nArchiv för Matemat., Astron. och Fys. 1, 681-702, 1904.\nHelge von Koch\\u2028(1870 –1924)\nwww.ComplexTrees.com\n",
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      "text": "www.ComplexTrees.com\n\n\\\"Les courbes planes ou gauches et les surfaces\ncomposées de parties semblales au tout. »\nJ. l'École Polytech., 227-247 and 249-291, 1939.\nPaul Lévy \\u2028(1886 –1971)",
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      "text": "r0 =\n\nr3\nLinear Extension\nof the Trunk\nLLL\nr1 =\nwww.ComplexTrees.com\nr n",
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      "text": "\nr = 0.61803…\n45º\n90º\n60°\n108°\nrSC =\nClassification of Fractal Trees\n135º\nwww.ComplexTrees.com\n120°\n144°\n180º\nrmin = ½ = 0.5\nrmax = 0.707…=",
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      "text": "1/Φ = Φ - 1= (1+√5 )½ - 1 ≈ 0.618…\n60°\nThe Beauty of Fractals: Six Different Views\nBy Dennis Gulick, Jon Scott MAA, Feb 28, 2011\n“Excursions Through a Forest of Golden Fractal Trees”\nTara D. Taylor, St. Francis Xavier University\n144°\n108°\n“Finding Gold in the Forest”\nwww.ComplexTrees.com\n120°",
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      "text": "The Beauty of Fractals: Six Different Views\nBy Dennis Gulick, Jon Scott MAA, Feb 28, 2011\n“Excursions Through a Forest of Golden Fractal Trees”\nTara D. Taylor, St. Francis Xavier University\nMathematical Details for the article of Frame & Mandelbrot\nSelf-Contacting Fractal Trees\nby Prof. Donald C. West © (1999)\nScaling Ratio\nr\nSelf-Contacting Binary Fractal Trees\nAngle θ\nTara D. Taylor\n“Computational Topology and Fractal Trees”,\nPhD Thesis, Dalhousie University, Canada (2005)\n\nwww.ComplexTrees.com\nhttp://faculty.plattsburgh.edu/don.west/trees/index.htm\nMichael Frame and Benôit B. Mandelbrot\nThe Mathematical Intelligencer, 1999 Springer-Verlag",
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      "text": "www.ComplexTrees.com",
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      "text": "www.ComplexTrees.com",
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      "text": "π/5 = 36°\n1/Φ ≈ 0.618…\nNonlinear Dynamics and Chaos:\nApplications in Atmospheric Sciences\nA.M.Selvam\nFig. 6. Quasicrystalline structure\nof the quasiperiodic Penrose tiling\npattern and Fibonacci sequence.\nA Hidden Golden Tree\nA Golden Cantor Set\nRoger L. Kraft\nThe American Mathematical Monthly,\nVol. 105, No. 8 (Oct., 1998), pp. 718-725\n\nwww.ComplexTrees.com",
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      "text": "Angle θ\nThe Complete Tip to Tip Contact Plot\n1/Φ = Φ - 1= (1+√5 )½ - 1 ≈ 0.618…\n",
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      "text": "\nAngle θ\nThe Complete Tip to Tip Contact Plot",
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      "text": "www.ComplexTrees.com\nHarmonic Fractal Trees\n",
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      "text": "www.ComplexTrees.com",
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      "text": "www.ComplexTrees.com\n",
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      "text": "www.ComplexTrees.com",
      "source_slide_id": "01DEB52B-B3AC-4B6F-A31F-26B9557A2C19",
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      "text": "“If you wish to advance into the infinite,\nexplore the finite in all directions.”\n⎯ Goethe.\nHolomorphic Dynamics Group\nNúria Fagella & Xavier Jarque\nwww.ComplexTrees.com\n@bernatree\nThank you!\nBernat Espigulé",
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      "text": ". . .",
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      "text": "“Our soul is composed of harmony, and harmony is never bred save in moments when the proportions of objects are seen or heard.”\n⎯ Leonardo da Vinci",
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      "text": "Harmonic Trees\n\n1/Φ = Φ - 1= (1+√5 )½ - 1 ≈ 0.618…",
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      "text": "\nHarmonic Trees\nImagen 5",
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      "text": "Symmetric Fractal Trees\nH. GÖTZE\n⎯ Castel del Monte, Gestalt und Symbol\nder Architektur Friedrichs II.\n3. Auflage Prestel, München 1991\n1991, Dr. Susanne Krömker\n",
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      "text": "\nSymmetric Fractal Trees\nImagen 5",
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      "text": "Imagen 2\nSymmetric Fractal Trees\n",
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      "text": "Imagen 7\nSymmetric Fractal Trees\n\nImagen 10\nImagen 6\nImagen 11\nImagen 12\nImagen 5\nImagen 8\nImagen 9",
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      "text": "Imagen 1",
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