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September 24 th 2010 West Wallsend High School Visit. Presentation by Jon Borwein, Director Centre for C omputer A ssisted R esearch M athematics and its A pplications. DOWNLOAD THIS PRESENTATION AT http://carma.newcastle.edu.au/outreach/. Fractals Everywhere. Mandelbrot Set.
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September 24th 2010West Wallsend High School Visit Presentation by Jon Borwein, Director Centre for Computer Assisted Research Mathematics and its Applications DOWNLOAD THIS PRESENTATION AT http://carma.newcastle.edu.au/outreach/
Fractals Everywhere Mandelbrot Set • What is a FRACTAL? • An image or curve which looks the same as you zoom in and out • What are some examples? • In software • On the internet • With paper,pencil, scissors • What are FRACTALS good for? • Scientific modelling: plant growth, viruses, erosion, … • Storage and bandwidth: send the menu not the meal • Art: movie forests, crowds, …. DOWNLOAD THIS PRESENTATION AT http://carma.newcastle.edu.au/outreach/ Jon Fractal
Self-Similarity Everywhere From BlaisePascal (1623-1662) to Sierpinski (1888-1969), Julia, Fatou and Benoit Mandelbrot (1924 - ) Truly modern mathematics in nature, art and applications ‘cut and fold, cut and fold’ DOWNLOAD THIS PRESENTATION AT http://carma.newcastle.edu.au/outreach/
www.cecm.sfu.ca/interfaces Deterministic and Random 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 21 7 1 Modulo 5 Real and Imaginary DOWNLOAD THIS PRESENTATION AT http://carma.newcastle.edu.au/outreach/
FRACTALINA How to create fractals in a program like fractalina math.bu.edu/DYSYS/applets/fractalina.html the chaos gamemath.bu.edu/DYSYS/applets/chaos-game.html reflection in more points (AARMS) The fern leaf fractal DOWNLOAD THIS PRESENTATION AT http://carma.newcastle.edu.au/outreach/
Chaos Games in Genetics Played with genetic rules on a square with Amino acids A, G, C and T DOWNLOAD THIS PRESENTATION AT http://carma.newcastle.edu.au/outreach/
Links for school and fun? • Pascal Triangle • its Sierpinski triangles • Sierpinski Triangle • randomly built • Sierpinski Carpet • squares, squares, … • Mandelbrot Set • how it is built • Super Fractals • Michael Barnsley’s (ANU) site • The Experimental Mathematics site • many more links • Fractal Cards • how to make them • Genetic Chaos Games • and Fractalina THANK YOU! Wilsons promontory (Va) DOWNLOAD THIS PRESENTATION AT http://carma.newcastle.edu.au/outreach/