September 24th 2010

West Wallsend High School VisitPresentation 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• 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, ….

Mandelbrot Set

Jon FractalDOWNLOAD THIS PRESENTATION AT http://carma.newcastle.edu.au/outreach/

From Blaise Pascal (1623-1662) to Sierpinski

(1888-1969), Julia, Fatou and Benoit Mandelbrot (1924 - )

Self-Similarity Everywhere

‘cut and fold, cut and fold’

Truly modern mathematics in nature, art and applications

DOWNLOAD THIS PRESENTATION AT http://carma.newcastle.edu.au/outreach/

www.cecm.sfu.ca/interfaces

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

Deterministic and Random

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How to create fractals in a program like fractalina math.bu.edu/DYSYS/applets/fractalina.html

the chaos game math.bu.edu/DYSYS/applets/chaos-game.html

reflection in more points (AARMS)

The fern leaf fractal

FRACTALINA

DOWNLOAD THIS PRESENTATION AT http://carma.newcastle.edu.au/outreach/

Chaos Games in Genetics

Played with genetic ruleson a square with Amino acidsA, 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

Wilsons promontory (Va)

THANK YOU!

DOWNLOAD THIS PRESENTATION AT http://carma.newcastle.edu.au/outreach/