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 fragmented geometric shape that can be split into parts,
e

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 numbers and Fractal
Geometry. Unlike the other dimensions -

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, the point is probably inside the
Mandelbrot set. If yo

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 images and resources are:
Frank Rousell's hyperindex of

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, there are two
functions, the left and right self-similar

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 segments. Now remove the middle thirds from the
remaining eig

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 in a year, beginning with a
single pair, if in every m

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 reflected in many types of
Electrical Networks. This paper co

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 math problems like this:
MMMCMXCVII MCMXCVIII = MCMXCI

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 knowledge to
discover the most effective ways of doing ma

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 will construct a set of rectangles using the Fibonacci

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 be produced in a year from a single pair if each pair p

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
Her hakk sakldr
ZET
Yksek Lisans Tezi
MANDELBROT CMLES VE TAR HES
Elif Aybike BYKYILMAZ
Ankara niversitesi
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