Fractal
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The Mandelbrot set is a famous example of a fractal
A closer view of the Mandelbrot set
A fractal is generally "a rough or fra
The Story of Benoit B. Mandelbrot
and the Geometry of Chaos
The story of Chaos begins in number, specifically in the mathematics and geometry
of the fourth dimension. This is the home of Complex numbe
11HowistheMandelbrotsetactuallycomputed?
The basic algorithm is: For each pixel c, start with z = 0.
Repeat z = z^2 + c up to N times, exiting if the magnitude of z gets
large. If you finish the loop,
Subject: The Mandelbrot set
Q6a : What is the Mandelbrot set?
A6a: The Mandelbrot set is the set of all complex c such that iterating z -> z^2 + c does not go
to infinity (starting with z = 0).
Other
Self-similarity
The Cantor set is the prototype of a fractal. It is self-similar, because it is equal to two copies
of itself, if each copy is shrunk by a factor of 3 and translated. More precisely, t
The Cantor Set
onsider a line segment of unit length. Remove its middle third. Now remove the
middle thirds from the remaining two segments. Now remove the middle thirds
from the remaining four segmen
The Fibonacci Sequence
edieval mathematician and businessman Fibonacci (Leonardo
Pisano) posed the following problem in his treatise Liber Abaci
(pub. 1202):
How many pairs of rabbits will be produced
Electrical Equivalence of discrete cascaded T sections,
Electrical Transmission Lines, and Fibonacci and Lucas
Numbers
Abstract - The Fibonacci numbers, Lucas numbers and the Golden Section are reflec
Thank You Leonardo Fibonacci!
.For making math easier!
I, Leonardo Fibonacci, wrote a famous book
that led to the widespread use of HinduArabic numerals. If I hadnt done that, you
might still be doing
Fibonacci Numbers
Leonardo Fibonacci was one of the great mathematicians of his
time. His lifestyle allowed him to travel and study math in various
countries, and he ended up combining his cultural kn
FIBONACCI IN NATURE
The Fibonacci numbers play a significant role in nature and in art and architecture.
We will first use the rectangle to lead us to some interesting applications in these
areas.
We
Fibonacci's rapidly-reproducing rabbits
Pages 404-405 of the English edition discusses the famous Fibonacci rabbit population
problem, which can be summarized like this:
How many pairs of rabbits can
ANKARA N VERS TES
FEN B L MLER ENST TS
YKSEK L SANS TEZ
MANDELBROT CMLES VE TAR HES
Elif Aybike BYKYILMAZ
MATEMAT K ANAB L M DALI
ANKARA
2009
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