1. Infinite Fractal Loop How do I use the Loop? What are fractals? How can I create fractals? More information about fractals About the Infinite Fractal Loop http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

2. Fractalus (Fractals/Fractal Art, Contests, And Info) Megasite dedicated to fractals. Artist Damien Jones, other artists, contests. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

3. Sprott's Fractal Gallery Daily updated gallery of automatically created fractals. Fractal generating software. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

4. Cynthia Lanius' Lessons A Fractals Lesson - Introduction Mathematics lessons for elementary school, middle school fractals, fractals, fractals http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

5. What Is A Fractal? When I first got the idea to learn about fractals, my impression, which may be similar to yours, was that it was a very advanced level of study and http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

6. Fractal Gallery What Is A Fractal? LarvasLeaf (105 k/ jpg) Fractals show us that the simplest engines of change often produce exquisitely elaborate patterns. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

7. Ultra Fractal Advanced Fractal Software Color your fractals and add transparency effects Compose fractals with multiple layers, masks, and Photoshoplike merge modes http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

8. Spanky Welcome The Spanky Fractal Database is a collection of programs, images, and other material all relating to the subject of Fractals http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

9. The Fractal Artists' Webring - Art. Not Dogma. Fractal Fun NEW! Fractals by Dekaro NEW! Perspix Fractals NEW! Fractals by Dekaro NEW! Perspix Fractals NEW! Beyond the Zero NEW! http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

10. Authorization Failure Galleries, puzzles, and screen savers. Javascript and Java enabled browsers required. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

11. Fractals And Music Most musicians have seen fractal imagesthose hauntingly beautiful picturesgenerated through mathematical equations. But how many people are aware that the http://emusician.com/mag/emusic_fractals_music/

var towercount = 0; var buttoncount = 0; var vertbannercount = 0; var smsquarecount = 0; var rectanglecount = 0; var spotlightcount = 0; var vertrectanglecount = 0; var lgsquarecount = 0; var bannercount = 0; var halfbannercount = 0; HOME PRODUCT NEWS FEATURE ISSUE EM SPOTLIGHT ... List Rentals Fractals and Music Gustavo Diaz-Jerez Oct 1, 1999 12:00 PM E-mail this article Most musicians have seen fractal images-those hauntingly beautiful pictures generated through mathematical equations. But how many people are aware that the same equations can be used to create hauntingly beautiful music? This article will explore fractals and discuss how they can be employed in musical composition. The technique is so versatile that you can use it to create music in any style, and it has great potential for adding an exciting new element to your music. Studying music from a mathematical point of view is nothing new; it dates back to ancient Greece. Around the fifth century B.C., Pythagoras uncovered mathematical relationships in music, in which musical intervals are represented as ratios of whole numbers. For example, the interval of an octave would be represented in the Pythagorean system as a 2:1 ratio because the frequency of the higher pitch is twice that of the lower. By the same system, the interval of a fifth would be 3:2, a fourth 4:3, and so forth. Other systems relating music to math have been developed, mainly in the 20th century. Among the many examples are Joseph Schillinger's System of Musical Composition and a method of composition developed by Olivier Messiaen in the 1940s. The more recent discovery of fractals and particularly their link to music has opened a door to composers, behind which lies immense creative possibility.

12. Fractals In Music fractals In music. A project by Edwin Vane for Dr. Will Gilbert s course Chaos and fractals have also been applied to music with varying degrees of http://www.cgl.uwaterloo.ca/~revane/chaos/main.html

Fractals In Music A project by Edwin Vane for Dr. Will Gilbert's course PMATH 370: Chaos and Fractals in the Faculty of Mathematics, University of Waterloo. Main Page White Music Brown Music 1/f Music Cantor Music ... Appendix Abstract This project will investigate several different methods for algorithmic composition of music. Three algorithms that produce music via random number methods are covered. These methods include White Music Brown Music , and 1/f Music . These methods are simple and produce only melodies. Two slightly more advanced algorithms are also considered for producing pleasing music where the purely random methods fail. These two algorithms include Cantor Music and IFS Accompaniment . These algorithms produce more complex (and pleasing) music with varying amounts of accompaniment and harmony. Summary and Background Chaos and Fractals appear in many forms throughout mathematics, art, and the world at large. Images of fractals (such as the one of the Mandelbrot Set to the right of the main title) are commonly known even outside the academic community. Fractals have been applied to image compression and to modelling real terrain in computer applications (for instance, fractal terrain generation in computer games). Chaos and Fractals have also been applied to music with varying degrees of success. Fractals, especially those generated via Iterated Function Systems, show varying degrees of self similarity. In the visual domain, this means that that the image of a fractal seen at one magnification is the same as the same fractal seen at a higher magnification (and perhaps at a different location). That is, fractals look the same close up as they do zoomed all the way out. A mountain looks (statistically) similar to a mound of dirt on the side of that mountain. A coast line seen from space looks (statistically) similar to that same coast line when viewed from a few feet away.

13. Fractals In Music fractals In music. A project by Edwin Vane for Dr. Will Gilbert s course PMATH370 Chaos and fractals in the Faculty of Mathematics, University of Waterloo http://www.cgl.uwaterloo.ca/~revane/chaos/cantorMusic.html

Fractals In Music A project by Edwin Vane for Dr. Will Gilbert's course PMATH 370: Chaos and Fractals in the Faculty of Mathematics, University of Waterloo. Main Page White Music Brown Music 1/f Music Cantor Music IFS Accompaniment Appendix The Cantor Set Background The Cantor Set is a well known self-similar fractal. It is created by taking an unbroken line and removing the middle third. The two line segments created from this removal are also subject to having their middle third removed. This process continues indefinitely. The cantor set looks the same at all levels of magnification which means it is strictly self-similar. Algorithm Consider the C Major triad: C-E-G. Take this as the straight line and remove the middle third to produce C-G. Then build triads off of each of these notes to produce C-E-G G-B-D. Removing the middle third of these two triads produces C-G B-D. The process continues by first building triads out of each of these four notes. The triad built on the last note of a sequence after the thirds have been removed (eg, D in the case of C-G B-D) will produce a new triad not already seen. In fact, if this process is continued long enough, every possible major triad can be achieved (The first few triads are D-F#-A, A-C#-E, E-G#-B and so on). Music can be created out of these triads. We will consider one iteration of this process as:

14. Fractals So how about music? Will fractal mathematics come to rescue in a time of apparent But when one investigates Ligeti s supposedly fractal music, http://www.notam02.no/~rolfwa/Fractalarticle.html

Rolf Wallin: Fractal Music - Red Herring or Promised Land? or "Just Another of those Boring Papers on Chaos" Lecture given at the Nordic Symposium for Computer Assisted Composition Stockholm 1989 (Oops - seems that the references to illustrations don't refer to any illustrations... sorry...) If the Vietnam war was the first TV war, the so-called Chaos theory must be the first commercially available scientific revolution, brought to a large public step by step. Chaos, fractals, Mandelbrot Sets, strange attractors, Cantor dust - these and some dozens other magical words have totally invaded popular science magazines during the 80's, accompanied by glossy colourprints of strange, disturbingly organical computergenerated shapes. However, this is just the shiny facade of a revolution that has left the international community of scientists of most diciplines at first totally dumbfounded by seeing central parts of their theoretical basis crumble, then completely frantic to investigate to what extent these scientific Columbi eggs can be applicable on their particular field. Fluid mechanics, geology, medicine, meteorology, in most fields many unsolvable problems have been solved by applying some part of this manyfaceted and bewildering bag of theories. Visual artists has also been attracted by the organical shapes that appear on the computer screens. So how about Music? Will fractal mathematics come to rescue in a time of apparent stagnation, this time in the guise of simple mathematical algorithms that yield delicious patterns that can be further processed, either as succession of musical events or as complex frequency spectra? The attempts to find an answer to this has barely begun. In the field of music the answers are not as selfevident as for the visual field. But this can actually turn out to be an advantage, if not technically, then at least aesthetically.

15. Compare Prices And Read Reviews On Fractals In Music: Introductory Mathematics F Epinions has the best comparison shopping information on fractals in MusicIntroductory Mathematics for Musical Analysis. Compare prices from across the http://www.epinions.com/Fractals_in_Music_Introductory_Mathematics_for_Musical_A

Join Epinions Help Sign In Books All Categories Home Media Books Fractals in Music: Introductory Mathematics for Musical Analysis Overall rating: This product has not yet been reviewed. We found this product at 2 stores The lowest base price is Write a Review Compare Prices View Details No Reviews Subscribe to reviews on this product Compare Prices Showing 1-2 of 2 stores Page 1 Sort by Store Name Sort by Store Rating Notes Sort by Price 1080 store reviews Pages: 210, Edition: 1st ed, Hardcover, High Art Press Get free shipping on orders over $25! Enter your ZIP for prices with tax and shipping. Price + Tax + Shipping = Total Price Your ZIP is used only to show applicable tax and shipping charges. at Amazon This store has not yet been rated. View store info Format: Hardcover Condition: New In stock at Alibris Showing 1-2 of 2 stores Page 1 Why are these stores listed? State Tax Only. Does not include local taxes. Shipping costs are estimates Please check merchant website for exact shipping costs. Featured Resources Additional information on Fractals in Music: Introductory Mathematics for Musical Analysis or other products. Musical Books Instructional books and videos. Free shipping on most items.

16. Applications Of Fractals - Fractal Music Today, there is a lot of fractal music software that allows you to play several Fractal music demonstrates basic idea of fractal music and even http://library.thinkquest.org/26242/full/ap/ap9.html

Applications of Fractals Fractal Music One of the very odd applications of fractals is turning geometric patterns into sound patterns. If you read the lesson on chaos and fractals , you already know that the simple formula new x = bx(1 – x) is capable of creating a fractal. For different values of b, we can see that the value of x changes differently. For some values, it stays at some fixed point, while for some it jumps between several values, and for others it jumps around chaotically. If you graph the value of x, you get something like this: If you now draw five lines through this graph and for every value of x put a note there, you will be able to play it as music. Choosing the right value for b, you can make music with a great variety of patterns. Today, there is a lot of fractal music software that allows you to play several patterns at the same time and choose different instruments. You can, for example, make some instruments play a non-repeating pattern and the other ones repeat a series of repeating notes. It isn’t Beethoven, but can still compete with many ultra-contemporary composers! Related Links: Fractal Music - demonstrates basic idea of fractal music and even displays notes.

17. Chaos And Fractals In Music Chaos and fractals in music. 4/5/01. Click here to start. Table of Contents.Chaos and fractals in music Introduction musical Properties Used http://www.science-house.org/student/bw/chaos/music/

Chaos and Fractals in Music Click here to start Table of Contents Chaos and Fractals in Music Introduction Musical Properties Used Rhythm ... Conclusions Author: Elizabeth Snoke Home Page: http://www.science-house.org/student/bw/chaos/ Download presentation source

18. Applications Of Fractals fractals AND music. Certain numbertheoretic sequences with fractal propertieshave been found to fractals in music, chapter 11 in CA Pickover (Ed.). http://www.stanford.edu/~jje/fractals/html/applications.html

by Jonathan Effrat MEDICAL APPLICATIONS OF FRACTALS Histopathology is concerned with the study of the morphological changes in cells and tissues during disease. These changes occur at the microscopic or submicroscopic level. Histopathology helps to interpret histological images (tissue samples) to make a diagnosis and selection of treatment. The earlier the diagnosis is made, the better the chances of successful treatment. The analysis and description of such complex and irregular morphologies is difficult and, to date, has been qualitative and subjective. These difficulties may be surmountable by using fractal geometry, which provides new approaches to objective measurement and understanding of shape complexity. Fractal geometry enables us to model and understand many physical and natural process that previously were considered irregular and patternless. We can use these “pathological” geometries to quantify morphological features of cells and tissues in order to differentiate between normal and pathological changes. (Landini 251-2) FRACTALS AND MUSIC Certain number-theoretic sequences with fractal properties have been found to generate appealing melodies and rhythms when the numerical data is transformed into musical notes and rhythmic patterns. Fractal designs have been used in composition, leading to melodies that, although purely mathematical in origin, sound surprisingly baroque. The analysis of music in terms of fractal patterns may lead to new insights in the classification of music. New musical instruments with fractal design features, such as drums with fractal perimeters, await exploration. (Schroeder 207)

19. Luminal.org - FMG it is theoretically possible to turn fractals into music and vise versa.The Fractal music Generator is my attempt to generate simple melodies based on http://www.luminal.org/wiki/index.php/Mag/FMG

Mag FMG SearchWiki Recent Changes ... Page History Fractal Music Generator (approve sites) by Mikhail Grigoriev Fractals and Music Music, especially classical music, relies heavily on repeating themes and self similarity. It is, for example, a common practice to use mathematical thransformations, such as temporal and pitch shifts, reversals and inversions, when writing cannons and fuges. Bach in particular was a master of this art. It is therefore not surprising that strong ties can be found between fractals and musical compositions. This leads one to believe that it is theoretically possible to turn fractals into music and vise versa. The Fractal Music Generator is my attempt to generate simple melodies based on well known fractal patterns. Fractal Music Generator The fractal music generator can be downloaded here The steps required to build it are as follows (tested only on Linux): 1. Obtain and build improv (approve sites) , a library for programming MIDI if you are using gcc 3.0 or higher, you will need to apply this patch to make it compile, like so:

20. Cecdiscuss: The International Electroacoustic Community Discuss fractal algorithms in music of 197090-s. I am aware of several techniques inmusic, such as fractals, as well as the cross-influence http://alcor.concordia.ca/~kaustin/cecdiscuss/1999/2572.html

fractals in music Subject: fractals in music From: Julia Dmitrioukova ( bach@cityline.ru Date: Wed Nov 17 1999 - 08:37:20 EST Next message: Teddy Hultberg: "Oyvind Fahlstrom On the Air - Again!" Previous message: Carlos Palombini: "Contact articles search" Next in thread: Dennis Miller: "Re: fractals in music" Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Greetings to all! I am a musicologist from Moscow State Conservatory (Russia). For my ongoing article, I am looking for information about significant examples of using fractal algorithms in music of 1970-90-s. I am aware of several important examples in the electronic field (Austin, Dodge...) but I still have no an exhausting view, as well as I know almost nothing about examples in non-electronic instrumental music (probably Ligeti used fractals in some works?). Can anybody help me with such an information (at least to mention any sources of it - books, articles etc.)? Thank you in advance. I also would be happy to be acquainted with serious specialists (both musicologists and composers), who develop the area of new algorithmic

A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z

Page 1     1-20 of 195    1  | 2  | 3  | 4  | 5  | 6  | 7  | 8  | 9  | 10  | Next 20