The document discusses the history and current understanding of mathematics, particularly focusing on fractal geometry as a new branch that describes complex patterns in nature. It highlights the discovery of beautiful patterns through simple rules and provides examples like the Sierpinski gasket and Koch snowflake. Additionally, it touches on the practical applications of fractals in fields such as film and technology.

2. • When was most of the maths you learn at GCSE discovered?
• A) Before 1700 B) Between 1700 and 1900 C) Since 1900
• How many pieces of new mathematics are published each year?
• A) 15-20 B) 1000 C) 250,000
• Mathematicians believe that there will be no new mathematics left
to discover by the year 2030 - True or False
• Mathematics Staff at university spend on average how many
hours teaching a week?
• A) 35 B) 25 C) 9

3. Fractal Geometry
Fractal Geometry
A new branch of mathematics

4. Phenomena in nature that can’t be
described using normal Geometry.

5. A new age in
computing
Complicated
patterns can be
plotted for the very
first time

6. By Michael Bradshaw
Mathematicians discovering that
repeating simple rules again and again
can produce wild and beautiful patterns

14. The Dragon Curve

15. Tiling the plane with the dragon
curve
Picture by Alexis Monnerot-Dumaine.

16. The Sierpinski gasket
• Your turn to recreate Sierpinski gasket
• And this is what is would look like if you
went one stage further:

17. What is a fractal????
• Often self similar
• However much you zoom in you still see a
pattern
• Often generated by a simple rule

18. What’s Special about the
Sierpinski Gasket?

19. Do other fractals have interesting
properties?
The Koch Snowflake

20. But are fractals actually useful?

21. But are fractals actually useful?
Yes!
e.g. in film
Image:Animated fractal mountain.gif - Wikipedia,
the free encyclopedia
A fractal landscape created by Professor
Ken Musgrave (Copyright: Ken Musgrave)

22. But are fractals actually useful?
and other egs:
fractal antenna
lungs