**Introduction to Fractals
and Iterated Function Systems (continued)**

Go Home. Go to Page contents near top of Page A1.

The following are some sites involving fractal
geometry and iterated function systems as garnered from the World
Wide Web. Some also involve * L-systems*
(see

My comments are in **black**.
Plagiarized text is in **maroon**.

**The following references to sites will
be sorted into a better arrangement by category later. **

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Web 1. **Fractals
and Chaos in Nature - Mark Cushman. Fractals and Chaos in Nature.
**http://the.cushman.net/reverb/fractals/ A general introductory essay.

Web 2. **See the glorious works of Ken
Musgrave via the** Ken Musgrave page.

**Web 3****. ****Fractal
Geometry and Multifractal Formalism.** Classical
mathematical concepts and methods are concerned with smooth
objects, ignoring irregular sets . . . Four
transformations in the plane are iterated as a random iterated
function system (IFS) to produce a fractal attractor of the
IFS -- in this case, a fern. Ignore for now the fine point about
which set of four probabilities produces the highest-fidelity
image. Note that you can see a blow-up of a leaf of the fern, and
it would be possible to generate a leaf of that leaf, and ., ad
infinitum -- all from 28 numbers!

**Here is how to grow a
fern! **

Start with a single rectangle.
Transform it into four smaller rectangles, suitably placed, and
all lying within (or mostly within) the original rectangle.
Denote these as transformations 1 to 4. Pick an arbitrary point
on the plane. Choose at random a digit from one to four. Apply
that numbered transformation to the point and plot the resulting
point. To that resulting point, apply the next randomly chosen
transformation. Repeat (iterate) this process several thousand
times. What you may see emerging from a supposedly random fog of
dots could be a pine tree or the famous * Black
Spleenwort Fern* of

Choose any portion of that image
and plot an additional million points to obtain as much
additional detail of the attractor as you wish. Whether one
started with four rectangles or four profiles of the Volkswagen
Beetle*, one will end up with the same image. Why? Because the
equations describing the transformations are invariant in
relation to the particular starting image (rectangle) used as
illustration. Iteration of the * ifs*
converges to its unique attractor. As an important refinement,
choose the transformations with probabilities that are relative
to the areas of their associated rectangles. This process is
referred to as the random iteration algorithm, or (by

*I love the VW Beetle ad: "Reverse engineered from UFOs"! (Demand now is so high that VW can't paste them together fast enough!)

**Have a look at what you
could have wrought!** http://ccaix3.unican.es/~gutierjm/fractals.html.

Web 303. **The
Fractory:** An Interactive Tool for Creating and Exploring
Fractals. This page will help you learn about fractals: what they
are and how to design them, but it will also let you discover
more on your own. Fractals are just now emerging as a science.
They show an order in seemingly random things, and give us tools
with which we can predict the weather, render natural looking
objects, and help understand the order in our chaotic lives. You
will also play a part in our interactive fractal creation center,
designing and displaying fractals you have invented. You can even
post your coolest fractals on our fractal message board. How to
Understand Fractals: **Fractals can be understood on many
different levels. We have separated the information on this page
into the five levels listed in increasing order of difficulty.**
http://library.thinkquest.org/3288/

Web 310.** ****Chaos in the Classroom.**
**Robert L. Devaney**, Department of Mathematics,
Boston University. Technology lets teachers bring some topics of
contemporary interest in research mathematics into both middle
school and high school classrooms. http://math.bu.edu/DYSYS/chaos-game/chaos-game.html

Web 315. ** ****Fractals page 1**
Fractals. Math Index, Index, A, B, C, . , Z. Ad Hoc Fractals. After landing on the site, start by clicking Mathematics
| Fractals. Has good tutorials. **A must-see site!** http://www.studyweb.com/math/fractal.htm

Web 320. **Here is one deep zoom. A big
image from the land of Mandelbrot.** It takes a while to
download, but it's worth it! It is probably a Julia set,
generated from z = z**2 + c (with z = x + i*y, iterated in the
complex plane. http://www.rosat.mpe-garching.mpg.de/fractals/bcad.gif

Web325.** ****Fractal Landscape Gallery** http://www.spence.net/ted/fractals/. Uses **KPT Bryce** software. See "* Jesse's
Cool Seascape*" for a rendition of a problem
that I have been considering: how to create waves and
reflectionson them.

Web 330. **Oliver's
images.** **Computer generated plants**
generated by our plant modelling software xfrog (http://www.greenworks.de/ ) (**see also Web 335 below**)
demonstrate the **state
of the art** in plant generation and imaging. These plants were generated by Marco
Bubke and rendered with Maya: **Computer generated
ecosystems** created in a project for SIGGRAPH 98 where we
showed that whole **ecosystems** can be generated
and rendered with today's workstations. The models were created
using **xfrog**, the populations were specified by
additional tools. The paper is: O. Deussen, P. Hanrahan, B.
Lintermann, R. Mech, M. Pharr, P. Prusinkiewicz: **Realistic
Modeling and Rendering of Plant Ecosystems **SIGGRAPH '98,
Orlando, Florida, July 19-24, 1998, http://isgwww.cs.uni-magdeburg.de/~deussen/gallery/gallery.html **Be
sure to see the final image of trees in a field of sunflowers --
among the finest of ****natural****
IFS images ever generated! Uses ****Xfrog****.
****See also
Web 335 below. **

Web
335. **Greenworks Organic Software,
Home of ****Xfrog****.**
**The organic modeler:** http://www.greenworks.de/ **Lintermann und Deussen Gbr**
and the **www.greenworks.de website** were launched
in 1996 in Karlsruhe Germany by **Bernd Lintermann**
and **Professor Oliver Deussen**, with the aim to
make their development efforts in the area of organic research
available to the general public, i.e., publish their technical
papers, and their software, * XFrog*.

**. . . Its
gallery! See also Web 330 above. **

**. . . Its ****documents****
section: , including:**

**. . . . .
. ****Interactive
Modelling and Animation of Branching Botanical Structures: **http://www.greenworks.de/greenWeb2/Templates/start.html** ****where you can see movies of
plants growing up!**

Web 340. **Sierpinski
Gasket: **http://www.swin.edu.au/astronomy/pbourke/fractals/gasket/** **The Sierpinski gasket
was originally described in two dimensions but represents a
family of objects in other dimensions. This family of objects
will be discussed in dimensions 1, 2, 3, and an attempt will be
made to visualise it in the 4th dimension. Along with a few cans of Coke! See also:

**. . . 3D Sierpinski
Gasket (3dsg.jpg): **http://www.povray.org/preview/irtc-cd3/stills/19970630/view/3dsg.htm** **

**. . . Sierpinski
Gasket: **http://www.agnesscott.edu/aca/depts_prog/info/math/riddle/ifs/siertri/siertri.htm** **

**. . . Sierpinski Gasket
Generator Applet: **http://www.rose-hulman.edu/~metzleda/Gasket.html** **Allows plotting lines, changing no. of
vertices.

**. . . The Sierpinski
Triangle Fractal: **http://www.best.com/~ejad/java/fractals/sierpinski.shtml** **Interactive Applet. **Go ahead and
play with it! Best demo of these! **

**. . . Sierpinski
Pyramid. **http://www.bearcave.com/dxf/sier.htm** **Variants.

**. . . The Magic
Sierpinski Triangle: **http://serendip.brynmawr.edu/playground/sierpinski.html** **Order dependent on
randomness. Interactive
Applet.

Web 360. **Fractals
and the Fractal Dimension. The Hausdorff Dimension: **http://www.vanderbilt.edu/AnS/psychology/cogsci/chaos/workshop/Fractals.html** **The "Richardson
Effect". Mandelbrot Set depicted with different colors or
altitudes. See also:

**. . . Felix Hausdorff: **http://turnbull.dcs.st-and.ac.uk/history/Mathematicians/Hausdorff.html** **In 1919 he introduced
the notion of * Hausdorff dimension*,
which was a real number lying between the topological dimension
of an object and 3. It is used to study objects such as

**. . . FRACTAL HISTORY
AND BACKGROUND. **http://www.digitallabyrinth.com/fractals/fractals.html** **The most intriguing of
the nonlinear fractals thus far has been the mathematical set
named after **Mandelbrot** by the American
mathematicians **John Hubbard** and **Adrien
Douady**.

**. . . Making Julia Set
Fractals:** http://www.lifesmith.com/makjulia.html * Julia
sets*, named for the early twentieth century French
mathematician

**. . . Abram
Samoilovitch Besicovitch: **http://www-groups.mcs.st-and.ac.uk/history/Mathematicians/Besicovitch.html** **His work on sets of
non-integer dimension was an early contribution to fractal
geometry. **Hausdorff**, in 1918, had extended **Carathéodory**'s
theory of measure to sets having finite measure of non-integral
order. **Besicovitch**, around 1930, extended his
density properties of sets to those of finite * Hausdorff
measure*. Domb writes:

Web 370. **Fractal
Geometry: **http://www.math.vt.edu/people/hoggard/FracGeomReport/index.html** **By John Hoggard.

Web 4.
**The World of Chaos.
Introduction. Laplace's Demon. **What is Chaos? The
Butterfly Effect. Strange Attractors. Logistic Difference
Equation. Fractals. Iterated **. . .** http://www.pha.jhu.edu/~ldb/seminar/ifs.html. Includes more on
how to generate the fern, etc.

Web 4000. **The
World of Chaos and Fractals. **This paper was written in
conjunction with a talk given for Intermediate Physics Seminar of
the Department of Physics and Astronomy at the Johns Hopkins
University. It provides an **excellent overview**,
being neither too vague nor too detailed. It includes the
following pages:

**. . . Introduction: **http://www.pha.jhu.edu/~ldb/seminar/index.html, including:

**. . . . . . Laplace's
Demon: **http://www.pha.jhu.edu/~ldb/seminar/laplace.html
Determinism.

**. . . . . . What is
Chaos? **http://www.pha.jhu.edu/~ldb/seminar/chaos.html
Chaos is **in**determinism at
its best.

**. . . The Butterfly
Effect: **http://www.pha.jhu.edu/~ldb/seminar/butterfly.html** **Weather prediction is difficult!

**. . . Strange
Attractors: **http://www.pha.jhu.edu/~ldb/seminar/attractors.html** ****Edward Lorenz** started
it!

**. . . Logistic
Difference Equation: **http://www.pha.jhu.edu/~ldb/seminar/logdiffeqn.html** **Variability in animal populations: a
simple quadratic equation, the logistic difference equation,
leads to fantastically complex and chaotic behavior.**
Bifurcation** and** Lorenz** and **Henon**
attractors.

**. . . Fractals: **http://www.pha.jhu.edu/~ldb/seminar/fractals.html** **Sierpenski triangle. Fractional
dimension. Snowflake curve of **Von Koch**.

**. . . Iterated Function
Systems (IFS): **http://www.pha.jhu.edu/~ldb/seminar/ifs.html** Black spleenwort fern.** This
image is infinitely complex -- a self-similar fractal on all
scales.

**. . . References: **http://www.pha.jhu.edu/~ldb/seminar/reference.html Books and more
links, including:

**. . . . . . **** The
Computational Beauty of Nature: a slide show: **http://mitpress.mit.edu/books/FLAOH/cbnhtml/slides.html

**. . . . . . ****The
Computational Beauty of Nature**** ****Computer
Explorations of Fractals, Chaos, Complex Systems, and Adaptation****,
**by Gary William Flake **: **http://mitpress.mit.edu/books/FLAOH/cbnhtml/home.html** **

**. . . . . . The Chaos
Hypertextbook: **http://hypertextbook.com/chaos/** ****Very detailed! **

**. . . . . . Chaos and
Order: **http://www.geocities.com/CapeCanaveral/Hangar/7959/** **

**. . . . . . Chaos &
Fractals: **http://library.thinkquest.org/3703/** **Part of the **ThinkQuest**
project. **Has Applets. **

**. . . . . . The Chaos
Experience: **http://library.thinkquest.org/3120/** **Includes real-life examples, e.g.,
washing machine.

**. . . . . . The Chaos
Metalink: **http://www.industrialstreet.net/chaosmetalink/** ****Optimized for WebTV! **

**. . . . . . fractalus
home: **http://www.fractalus.com/home/** **Over three hundred and ninety fractal
images + . . .

**. . . . . . Mu-Ency -
The Encyclopedia of the Mandelbrot Set: **http://www.mrob.com/muency.html** **

Web 5. **J.P.
Louvet : Fractals - A History. The discovery of fractals. **http://www-hs.iuta.u-bordeaux.fr/louvet/history.html 8-Feb-98. **Excellent pics.**** **

Web 6. **No
Title A Path to Fractals. **Nature is filled with a beauty
easily perceived at many levels. Trees and forests, rocks and
mountains, streams and mighty rivers, http://fas.sfu.ca/0/cs/research/projects/FractalCal/trade96/essay.html 8-Mar-95. No pics.

Web 7. **Fat
Days: Fractal Links. Spanky Fractal Database. **Huge archive of fractal-related programs, . . . http://www.fatdays.com/fractals/FractalLinks.html

Web 400. **Open
Directory - Science Math Chaos and Fractals. **Excellent
links to Chaos and Fractals (184 links), Chaos (44), Fractal Art
(77), and Software (30). http://www.dmoz.org/Science/Math/Chaos_and_Fractals/ Here are some:

**. . . The Computational
Beauty of Nature:** **Computer Explorations of Fractals,
Chaos,
Complex Systems, and Adaptation. **http://mitpress.mit.edu/books/FLAOH/cbnhtml/

**. . . Fractals: **http://www.calweb.com/~bjohnson/fract.html** **An excellent site with
in-depth descriptions of many different types of fractals. It
also describes the formulas behind the creation of the fractals.

**. . . Our Fractal
Universe:** http://library.thinkquest.org/25810/# See **Fractals in Nature |
Fractals in Biology **for interesting relationship between
animal size, metabolic rate, and fractals. Good overview of IFS
basics and of advanced IFS image compression via range and domain
blocks.

**. . . ****Fantastic
Fractals.**** **A comprehensive fractals site that
features tutorials for all ages, fractal-generated music,
realistic landscapes. Our Fantastic Fractals 98 software that can
generate millions of fractals is available for download only at
this site. Interact with others through the fractal workshop,
message boards, and discussion forum. **http://library.thinkquest.org/12740/cgi-bin/login.cgi****
**

**. . . Fractal
Adventures. **Helps the beginner to create fractal images.
Overview of programs. Program-related fractal Gallery. http://home.att.net/~Novak.S/

**. . . Fractals:
Nature's Numbers?** http://www.cs.sfu.ca/people/GradStudents/darylh/personal/images/present/nat-num/

**. . . Fractal Seeks
Wavelet.** A research project for De MontfortUniversity,
exploring links between ** Fractals** and

.**. . . Fractals
Unleashed.**.http://library.thinkquest.org/26242/ **The
most comprehensive website about fractals on the net.**
Contains **enourmous amounts of information**,
including fractal applications, Java applets, CGI programs, a
well-organized gallery, and a fractal art contest. Download
software and learn how to program fractals too!

**. . . An Introduction
to Fractals.** http://codenet.al.ru/progr/fract/intro.htm Gives
excellent description, math, image of fern, and C-code to
generate it. Slow to download (from Russia with love), but **worth
it! **

Web 410. **Chaos
Web Site -- Fractals and Resources: **http://inst.santafe.cc.fl.us/~honors/chaosweb/fractals.htm**. Includes many links,
including: **

**. . . Interactive
Fractal Servers, including: **

**. . . . . . Mandelbrot
Viewer: **http://www.mindspring.com/~chroma/mandelbrot.html** **with interactive Java Applet.

Web 14. **IFS
A general, way to generate fractals is through Iterated Function
Systems (****IFS****s). **

http://math.bu.edu/DYSYS/applets/fractals/IFSs/IFSs.html 5-Sep-97 See some of the math. and try your own * ifs*!

Web 15.** ****Fractal Image Compression** http://www.rasip.fer.hr/research/compress/algorithms/adv/fraccomp/. Here is your chance to meet **Lena**!
This site has excellent details of IFSs and images of **Lena**,
including an example of a compressed image having more detail of
her than the original -- not to be missed! No other compression
technique (e.g., JPEG, MPEG, GIF) can do this because, although
non-* ifs* compression techniques, and
even the direct rendition of the original image, are
pixel-dependent, the

Web 16. **Fractal
Image Compression: **http://www.rasip.fer.hr/research/compress/algorithms/adv/fraccomp/index_hr.html. More math. -- and another look at **Lena**!

Web 17. **Groupe
Fractales - INRIA. Fractal approaches for the analysis and
modeling of complex signals.** Fractal approach for
studying complex systems have proven useful in mathematics . . . http://www-syntim.inria.fr/fractales/Equipe.html.

Web 19. **Iterated
Function Systems, Technical Description, based on the extended
mathematical development given in Barnsley's 1988 . . .** http://cogsci.ucsd.edu/~arobert/ifstech.html More math!

Web 20. **Fractal
Image Compression. Michael Barnsley and Lyman Hurd ISBN
1-56881-000-8. AK Peters - 1993 Hardcover 254pp $54.95.** How to encode 7
hours of sound, 100 animations, 800 color maps and more than 7000
photographs in less than 600 megabytes of data on a single
computer compact disk. http://www.ippi.com/dir_akp/akp_fracim.html. Encarta.

Web 22. **Fractals
link between the sculpture Temple of Fire of John Robinson and
the world of fractals. **http://www.bangor.ac.uk/SculMath/image/tetra.html.

Web 1220. **Center
for Polymer Studies** (CPS), a scientific visualization
research center in the Physics Department and Science and
Mathematics Education Center at Boston University, devoted to
interdisciplinary research in polymer, random, and fractal
systems. http://polymer.bu.edu/. Natural
images, molecular dynamics. **Excellent!**

Web 1224. **Recursion:
A Paradigm For Future Music?** Potential uses of
recursion, iteration and complex mathematics as an extension of
traditional music-compositional practice. Includes an elementary
introduction to fractal-related tools proposed to be useful for
extrapolating new sequences of musical events. http://www-ks.rus.uni-stuttgart.de/people/schulz/fmusic/recursion.html

Web 1226. **Chaos
and Music Ames, C. "****Stylistic Automata
in Gradient****".** Computer Music
Journal Vol. 7, No. 4, 1988 http://www.evl.uic.edu/EVL/VROOM/HTML/PROJECTS/57Bargar.cm.html Bibliography and
extensive links.

Web 1260. **Fractal
Music Project.** Fractals provide extremely interesting
musical results, and the field is becoming one of the the most
exciting fields of new music research. Fractal music enthusiasts
are encouraged to publish their works here. http://www-ks.rus.uni-stuttgart.de/people/schulz/fmusic/
Has Links ( http://www-ks.rus.uni-stuttgart.de/people/schulz/fmusic/links.html ) to physics, mathematics, algorithms
and artificial intelligence.

Web 1270. Fractal
music. **CLASSIFYING** music using fractals could make it much
easier for Internet search engines to pick out the kind of music
people are looking for, say researchers in France. Scientists
have long looked for self-similar patterns, or fractals, in music
but without much success. Alain Iost and Maxime Bigerelle at the **University
of Science and Technology in Lille**, France, made their
breakthrough by looking at the amplitude of notes--their
loudness--rather than their pitch. They found that the fractal
patterns in the way loudness varies could be used to distinguish
between different types of music, such as heavy metal and jazz.
From** New Scientist magazine**, 05 August 2000. http://www.newscientist.com/news/news_225039.html

Web 27. **Complex
Systems:** The last few years have seen extraordinary
growth of interest in complex systems. From ecology to economics
. . . http://physics.hallym.ac.kr/education/chaos/green/complex.html. Excellent images, especially by Junpei Sekino after
clicking on "various pretty fractal pictures". Has
great math intro.!

Web 28. **Brighten
Godfrey's Web Site! Fractals, Funnies, and more:** http://www.bigw.org/~godfreyb/ . **Don't miss the "Humor" section!**

Web 29. **NeuroFractal
Home Internet Centre of Excellence:** srl is an all
azimuth WWW consulting company based in Milan, Italy. http://www.icenet.it/icenet/neurality/neurofractal/neurofractal_home_uk.html. Imputation of
IFSs via neural nets -- an interesting concept! How a **neural network, learning**
from a set of points plotted by the Chaos algorithm, is able to
generate fractal shapes (a fern). In the second study, a neural
network tries to reconstruct the IFS functions starting from the
lighted pixels in a raster image. This is a first, rough
tentative to reach the fractal image compression through neural
networks. **Excellent
ideas!**

Web 30. **Fractal
Image Compression Bibliography: **http://www.dip.ee.uct.ac.za/~brendt/bibliographies/html/fractal_coding.html.

Web 506.** ****The Fractal Art of Uwe Krueger
and Heinz Wolf **

http://www.fractals.com/fractal_gallery/uwe_krueger/room1.html. Two pioneers of image rendering. All of their rooms (1
to 4, at least) are must-see! . http://www.fractals.com/fractal_gallery/uwe_krueger/room4.html A must-see site! More images from Mandelbrot country,
all from z = z**2 + c! Linkages
obsolete. Looking for new ones.

Web 34. **Fractal
Art Umbrellas Order Form. Shaw Creations. **http://www.lifesmith.com/umbrella.html How to get noticed on a rainy day! Not warranted for
use atop bowler hats in London!

Web 35. **Fractal
Art Jigsaw Puzzles: **http://www.lifesmith.com/puzzles.html. Be puzzled no
longer!

Web 38. **Fractal
- Art Gallery - David Neal Dubois:**
http://www.zelkop.com/fractal.html. See "* The story behind
the image*" for a simple explanation of how to
generate Mandelbrot sets.

Web 41. **Spanky
Welcome THE SPANKY FRACTAL DATABASE. The Elastic Fractal. **http://spanky.triumf.ca/www/welcome1.html **A major database! **

Web 42. **THE
FRACTAL DATABASE **(a large portion is mirrored from
spanky). The capillary Fractal. Fractals and scale. A tutorial on
. . . http://egnatia.ee.auth.gr/~ngramm/fractals/ **A major database!!! **

Web 46. **Fractals
& the Set. Explanation of Fractals and the Mandelbrot Set**,
using material from Chan 4 program with Arthur C. Clarke. http://www.unity.force9.co.uk/fractals/ This page is intended to be a basic introduction to
Fractal Geometry, and more specifically the Mandelbrot Set, aided
by material from a television program presented by Arthur C.
Clarke, Colours of Infinity. **Well worth a visit! **

Web 47. **Gumbycat's
Cyberhome** - For Scott: http://wizzle.simplenet.com/linda/define/fractals_defined.htm

Web 48. **A big image from the land of
Mandelbrot: **http://www.rosat.mpe-garching.mpg.de/fractals/bcad.gif . **It takes a while to download, but it's worth
it! Talk about sunflowers! **

Web 49.**Fractint
Fractal Gallery:** http://spanky.triumf.ca/www/fractint/fract-gal.html
**Well worth a visit! **

Web 50. **Weed's
Fractal Gallery:** http://www.venus.co.uk/~weed/fractals/welcome.html See the flaming brot (Weed). **Well worth a
visit! **

Web 51. **Fractint
WWW pages.** **Fractint** is a **freeware**
fractal generator created for IBM PCs and compatible computers.
It is the most versatile and extensive fractal program available
for any price. http://spanky.triumf.ca/www/fractint/fractint.html

Web 52.**
Iterated Systems:** http://www.iterated.com/ The corporate home of **Michael Barnsley**,
inventor of * iterated function systems*,
co-founder of

Web 55. **Jay
Hill's Home Page:** http://www.geocities.com/CapeCanaveral/Lab/3825/index.html

Web 57. **Fractal
Web Sites:** http://www.io.com/~stephens/FractalWebs.html **Extensive, excellent links. **

Web 58. **Brain
Games Web Guide:** http://thinks.com/webguide/fractal.htm **See the works of Ken (not Forest) Musgrave, a
pioneer of fractal landscape art and fractal planets! Extensive,
excellent links. **

68. **Graphics
Archive -- Clouds 3** by Danek Duvall is one of four
created using spectral . . . http://www.geom.umn.edu/graphics/pix/General_Interest/Fractals/Clouds/cloud3.html. **How to
draw a cloud!**

Web 77. Member
of Faculty **Dr. Richard Voss**. Professor of
Complex Systems and Brain Sciences. Professor of Physics and
Mathematics: voss@walt.ccs.fau.edu. http://www.fau.edu/divdept/physics/staff/voss.htm

Web 620. **Cut
The Knot!** **An interactive column using Java
applets by Alex Bogomolny****. The Collage
Theorem.** http://www.cut-the-knot.com/ctk/ifs.html
Has detailed math. Alex Bogomolny has started and still
maintains a popular Web site Interactive
Mathematics Miscellany and Puzzles to which he brought more than 10 years
of college instruction and, at least as much, programming
experience. He holds M.S. degree in Mathematics from the Moscow
State University and Ph.D. in Applied Mathematics from the Hebrew
University of Jerusalem. **Broad educational resources.
Lets you produce and plot your own *** ifs*s

Web 658. **Sites
- Implicate Beauty:** A Computational Art site: visitors
are invited to draw curves . . . http://www.west.it/ensites/ib.htm **Includes conversion of Mandelbrot set into
music! **

Web 1070. **Benoit
Mandelbrot CONFERENCE ON A NEW SPACE FOR CULTURE AND SOCIETY.
(NEW IDEAS IN SCIENCE AND ART). **http://pconf.terminal.cz/participants/mandelbrot.html **About Mandelbrot and lecture by him. Must see! **

Web 81. **Huge
Harry, Institute of Artificial Art, Amsterdam, advocates complete
automatization of art generation.** He works with Arthur
Elsenaar on computer-controlled facial expression and http://www2.netcetera.nl/~iaaa/hhpub.html Faces and music.

96. **algo
Algorithmic composing. **http://midiworld.com/qe2/paul/algo.htm 10-Jan-97. Some links to unusual and/or useful tools: •Algorithmic Art •Fractal
Music Project •Koan Pro •Seq303 •Aleatoric
composer •Anklung

Web 500. **IFD:
Internet Fractal Database.**The database contains **112
galleries** and a list of resources to find more
galleries. http://www.ba.infn.it/~zito/project/gallerie.html
**Excellent site! **

Web 117. **Evolutionary
Computation**** ****and its application to art and
design:** behavior control programs for artificial
agents. http://www.red3d.com/cwr/evolve.html

Web 61. **Carlson's
Fractal Gallery:** http://sprott.physics.wisc.edu/carlson.htm

Web 66. **FRACTAL
LANDSCAPE 2 Emergency Exit** / Sortie de Secours. Page
maintained by FLEETOX, © DMHK. Created: Tue 14 May 96 Ud:
11-06-96. http://www.micronet.fr/~jeephk/flee2.htm Getting closer to the type of landscape that I would
like to build -- in this case, mountains!!! **Excellent!**
See more landscapes at: http://www.micronet.fr/~jeephk/flee3.htm , http://www.micronet.fr/~jeephk/flee6.htm ,
etc. or use navigator at site.

Web 69. **Fractal
Landscape Gallery **http://www.spence.net/ted/fractals/ Uses **KPT Bryce** software! See * Jesse's
Cool Seascape* for a rendition of a problem that I
have been considering: how to create waves and reflections on
them.

Web 72. **Chaos
and Fractals : New Frontiers of Science**, by Heinz-Otto
Peitgen, Hartmut Jurgens, Dietmar Saupe, H. O. Peitgen, E.
Maletsky, L. Yunker: http://www.amazon.com/exec/obidos/ISBN=0387979034/gmsuA **The big book. A treasure!!!**

Web 73. **Fractal
Imaging: **ISBN: 0124580106 Academic Press Publ Mar 97.
Pages: 441 Price: £ 34.95 Author: Ning Lu..http://www.harcourt-international.com/catalogue/title.cfm?ISBN=0124580106

KEY FEATURES * Focuses on

fractal imaging using affine transformations* Applies various applications toreal-world photographic imaging* Presents a new image model, 'image as a distribution', for the first time * Examines information on all current compression technologies * Includes a CD-ROM containing fractal images and a freeware version ofIterated Systems' fractal imaging utility * Describes why the fractal method gives a good model with respect to the human visual system *Foreword by Michael Barnsley* Projects key developments in the future of fractal optical image capturing devices

CONTENTS: Introduction. Mathematical Foundation. Fractal Imagery Model. Image Spatial Mask. Spatial Parameters. Brightness and Contrast. Clustering Searching. Decompression Techniques. Image in Motion. Color Image. Entropy Copy. Imagery Applications. Further Enhancement.

Fractal Image File Format. Future Fractal Imagery.

Web 573.** ****Laboratory of Eidomatics.
Visitate il Museo Nazionale della Scienza** **e
della Tecnica di Milano!**

Reaearch topics: **Photorealism.**
Accurate photometric modelling, optimisation and parallelisation
of ray-tracing and radiosity algorithms; **Volume
Rendering.** EVA-VisualStudio: an interactive system for
Volume Visualisation, Analysis and Classification; **Visualization
of Digital Terrain** Models; **Colour Visual
perception** Computer simulation of Edwin Land's Retinex
Model; **Fractal Image Compression**. Yet another
implementation of IFS image compression; **Object Oriented
geometric modelling and construction.** GEObject: an
object oriented system for interactive geometric modelling and
geometric construction, that mimics plane constructive euclidean
geometry.

http://mercurio.sm.dsi.unimi.it/~marini/imaging/HOME.html

End of part 1 of 3 of section 10. Web Sites. _______ Continued
at part 2 of section 10.
Web Sites, at Page A4.** **

Go Home. Go to Page contents near top of Page A1.

You can e-mail me at waynerp@sympatico.ca