无处不在的分形

所属分类:数学  
出版时间:2009-1   出版时间:世界图书出版公司   作者:巴恩斯利   页数:531  
Tag标签:分形,数学,物理,非线性,科普,教材,思维  

内容概要

Credlts for Figures and Color Plates Much has changed in the world of fractals, computer graphics and modem mathematics since the first edition of Fractals Everywhere appeared. The company Iterated Systems, Inc., founded by Michael Barnsley and Alan Sloan, is now competing in the image compression field with both hardware and software products that use fractal geometry to compress images. Indeed, there is now a plethora of texts on subjects like fractals and chaos, and these terms are rapidly becoming "household words.

作者简介

作者:(英国)巴恩斯利 (Barnsley.M.F)

书籍目录

Foreword.AcknowledgmentsChapter

IntroductionChapter

Metrlc
Spaces;
Equlvolent
Spaces;
Clossificatlon
of
Subsets;
and
the
Space
of
Froctols
1.Spaces
2.Metric
Spaces
3.Cauchy
Sequences,
Limit
Points,
Closed
Sets,
Perfect
Sets,
and
Complete
Metric
Spaces
4.Compact
Sets,
Bounded
Sets,
Open
Sets,
Interiors,
and
Boundaries
5.Connected
Sets,
Disconnected
Sets,
and
Pathwise-
Connected
Sets
6.The
Metric
Space
(74(X),
h):
The
Place
Where
Fractals
Live
7.The
Completeness
of
the
Space
of
Fractals
8.Additional
Theorems
about
Metric
SpacesChapter

Transformations
on
Metric
Spaces;
Contraction
Mappings;
and
the
Construction
of
Fractals
1.Transformations
on
the
Real
Line
2.Affine
Transformations
in
the
Euclidean
Plane
3.MObius
Transformations
on
the
Riemann
Sphere
4.Analytic
Transformations
5.How
to
Change
Coordinates
6.The
Contraction
Mapping
Theorem
7.Contraction
Mappings
on
the
Space
of
Fractals
8.Two
Algorithms
for
Computing
Fractals
from
Iterated
Function
Systems
9.Condensation
Sets
10.How
to
Make
Fractal
Models
with
the
Help
of
the
Collage
Theorem
11.Blowing
in
the
Wind:
The
Continous
Dependence
of
Fractals
on
ParametersChapter

Chaotic
Dynamics
on
Fractals
1.The
Addresses
of
Points
on
Fractals
2.Continuous
Transformations
from
Code
Space
to
Fractals
3.Introduction
to
Dynamical
Systems
4.Dynamics
on
Fractals:
Or
How
to
Compute
Orbits
by
Looking
at
Pictures
5.Equivalent
Dynamical
Systems
6.The
Shadow
of
Deterministic
Dynamics
7.The
Meaningfulness
of
Inaccurately
Computed
Orbits
is
Established
by
Means
of
a
Shadowing
Theorem
8.Chaotic
Dynamics
on
FractalsChapter

Fractal
Dimension
1.Fractal
Dimension
2.The
Theoretical
Determination
of
the
Fractal
Dimension
3.The
Experimental
Determination
of
the
Fractal
Dimension
4.The
Hausdorff-Besicovitch
DimensionChapter

FrocIoI
Interpolation
1.Introduction:
Applications
for
Fractal
Functions
2.Fractal
Interpolation
Functions
3.The
Fractal
Dimension
of
Fractal
Interpolation
Functions
4.Hidden
Variable
Fractal
Interpolation
5.Space-Filling
CurvesChapter

Julia
Sets
1.The
Escape
Time
Algorithm
for
Computing
Pictures
of
IFS
Attractors
and
Julia
Sets
2.Iterated
Function
Systems
Whose
Attractors
Are
Julia
Sets
3.The
Application
of
Julia
Set
Theory
to
Newton's
Method
4.A
Rich
Source
for
Fractals:
Invariant
Sets
of
Continuous
Open
MappingsChapter

Parameter
Spaces
and
Mandelbrot
Sets
1.The
Idea
of
a
Parameter
Space:
A
Map
of
Fractals
2.Mandelbrot
Sets
for
Pairs
of
Transformations
3.The
Mandelbrot
Set
for
Julia
Sets
4.How
to
Make
Maps
of
Families
of
Fractals
Using
Escape
TimesChapter

Measures
on
Fractals
1.Introduction
to
Invariant
Measures
on
Fractals
2.Fields
and
Sigma-Fields
3.Measures
4.Integration
5.The
Compact
Metric
Space
(79(X),
d)
6.A
Contraction
Mapping
on
(P(X))
7.Elton's
Theorem
8.Application
to
Computer
GraphicsChapter

Recurrent
Iterated
Function
Systems
1.Fractal
Systems
2.Recurrent
Iterated
Function
Systems
3.Collage
Theorem
for
Recurrent
Iterated
Function
Systems
4.Fractal
Systems
with
Vectors
of
Measures
as
Their
Attractors
5.ReferencesReferencesSelected
AnswersIndex

章节摘录

插图:

编辑推荐

《无处不在的分形(第2版)》由世界图书出版公司出版。

图书封面

图书标签Tags

分形,数学,物理,非线性,科普,教材,思维


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