west wallsend high school visit september 24 th 2010 west wallsend high school visit presentation by...
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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
DOWNLOAD THIS PRESENTATION AT http://carma.newcastle.edu.au/outreach/
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/