West Wallsend High School Visit September 24 th 2010 West Wallsend High School Visit Presentation by...
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September 24 th 2010 West 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/
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Transcript of West Wallsend High School Visit September 24 th 2010 West Wallsend High School Visit Presentation by...
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/
