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Chaos and Fractals: New Frontiers of Science

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Almost 12 years have passed by since we wrote Chaos and Fractals. At the time we were hoping that our approach of writing a book which would be both accessible without mathematical sophistication and portray these exiting new fields in an authentic manner would find an audience. Now we know it did. We know from many reviews and personal letters that the book is used in a w Almost 12 years have passed by since we wrote Chaos and Fractals. At the time we were hoping that our approach of writing a book which would be both accessible without mathematical sophistication and portray these exiting new fields in an authentic manner would find an audience. Now we know it did. We know from many reviews and personal letters that the book is used in a wide range of ways: researchers use it to acquaint themselves, teachers use it in college and university courses, students use it for background reading, and there is also a substantial audience of lay people who just want to know what chaos and fractals are about. Every book that is somewhat technical in nature is likely to have a number of misprints and errors in its first edition. Some of these were caught and brought to our attention by our readers. One of them, Hermann Flaschka, deserves to be thanked in particular for his suggestions and improvements. This second edition has several changes. We have taken out the two appendices from the firstedition. At the time of the first edition Yuval Fishers contribution, which we published as an appendix was probably the first complete expository account on fractal image compression. Meanwhile, Yuvals book Fractal Image Compression: Theory and Application appeared and is now the publication to refer to.


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Almost 12 years have passed by since we wrote Chaos and Fractals. At the time we were hoping that our approach of writing a book which would be both accessible without mathematical sophistication and portray these exiting new fields in an authentic manner would find an audience. Now we know it did. We know from many reviews and personal letters that the book is used in a w Almost 12 years have passed by since we wrote Chaos and Fractals. At the time we were hoping that our approach of writing a book which would be both accessible without mathematical sophistication and portray these exiting new fields in an authentic manner would find an audience. Now we know it did. We know from many reviews and personal letters that the book is used in a wide range of ways: researchers use it to acquaint themselves, teachers use it in college and university courses, students use it for background reading, and there is also a substantial audience of lay people who just want to know what chaos and fractals are about. Every book that is somewhat technical in nature is likely to have a number of misprints and errors in its first edition. Some of these were caught and brought to our attention by our readers. One of them, Hermann Flaschka, deserves to be thanked in particular for his suggestions and improvements. This second edition has several changes. We have taken out the two appendices from the firstedition. At the time of the first edition Yuval Fishers contribution, which we published as an appendix was probably the first complete expository account on fractal image compression. Meanwhile, Yuvals book Fractal Image Compression: Theory and Application appeared and is now the publication to refer to.

30 review for Chaos and Fractals: New Frontiers of Science

  1. 4 out of 5

    Cara

    Bruh. I don't think I understood most of what I read, but I really just did that. I read that whole textbook. Bruh. I don't think I understood most of what I read, but I really just did that. I read that whole textbook.

  2. 5 out of 5

    Paige McLoughlin

    This is a book I read or skim or have varying levels of engagement with each time I pick it up. I always get something new from it. Fractals, Chaos, and Power laws started getting my attention in the late 80s in my deadhead days. The patterns created jived well with my psychedelic aesthetic at the time and I became intrigued by the subject and have had an eye out for books on it ever since.It seems nature quickly tired of the boring old geometry of Euclid (circles and triangles only take you so This is a book I read or skim or have varying levels of engagement with each time I pick it up. I always get something new from it. Fractals, Chaos, and Power laws started getting my attention in the late 80s in my deadhead days. The patterns created jived well with my psychedelic aesthetic at the time and I became intrigued by the subject and have had an eye out for books on it ever since.It seems nature quickly tired of the boring old geometry of Euclid (circles and triangles only take you so far) but an iteration of fleas being bitten by smaller fleas who in turn are bitten by smaller fleas and so on. The power of iteration seems to be a powerful form generator in nature and she uses it all the time. Using mixing as well another character that nature adores deterministic Chaos aka the butterfly effect where a system that starts with extremely close initial conditions soon diverges unpredictably. It is the reason why weather forecasting is pretty much useless extrapolating a week or two out into the future. And my favorite persona comes on stage the Mandelbrot another set of points that is created by a simple iteration process that generates infinite complexity and intricate beautiful patterns it is exhibit A for Plato's heavenly form. So little goes in to generate so much. Books like this get me to overcome my laziness and engage with the math. A well I draw upon often.

  3. 4 out of 5

    Walter

    Chaos theory is one of the most powerful and least understood paradigms to have emerged in natural science in the last 50 years. Developed in the 1980s and expanded in the 1990s, Chaos theory challenges the notion that complex processes that scientists see in such fields as physics, geology, biology and economics are not the results of random processes but are actually deterministic phenomena, the result of complicated conditions. The exciting part of this theory is that, unlike stochastic pheno Chaos theory is one of the most powerful and least understood paradigms to have emerged in natural science in the last 50 years. Developed in the 1980s and expanded in the 1990s, Chaos theory challenges the notion that complex processes that scientists see in such fields as physics, geology, biology and economics are not the results of random processes but are actually deterministic phenomena, the result of complicated conditions. The exciting part of this theory is that, unlike stochastic phenomena, processes that arise from deterministic conditions are, at least theoretically, able to be modeled, and thus predictable. This idea has breathed new life into scientific inquiry into a number of fields. This book is a good and easy to read introduction to Chaos Theory and the Fractal Geometry that illustrates it. Peitgen explores the basic assumptions of Chaos Theory; the dependence on intial conditions, the non-linear dynamics that characterise it, and the effects of earlier observations of a phenomenon on its later direction. The mathematics of this theory are complicated, but Peitgen introduces the basic concepts of chaos theory in a way that the non-sophisticated mathematician can understand. He does this in a very readable and compelling way. Another fascinating aspect of this work is Peitgen's exploration of Fractal Geometry. Fractals are geometric shapes that include complicated spurs, peaks and other irregularities that one does not see in the neat lines, angles and arcs of Euclidian geometry. Peitgen illustrates the geometry of some of the processes that he maps out with beautiful maps of Fractal shapes. His illustrations show us how these processes can result in the kind of complex but beautiful shapes that we see in crystals, plants, shorelines and other natural occurances. These shapes also lend credence to the theory that Chaos processes could have led to the generation of some of these natural phenomena. Pietgen further illustrates his topics with classical theories from some of the greatest scientists and mathematicians in history. Men like Blaise Pascal, Raul Julia and Benoit Mandelbrot have advanced theories in their times that have contributed to Chaos theory, so the reader can understand that Chaos theory was not pulled out of some theoretical hat. Furthermore, after every chapter, Peitgen lays out a Basic program that generates some of the processes and shapes that Peitgen describes in the chapter. If the reader can plug these short programs into a Basic compiler, he can visually see the concepts that Peitgen is teaching him. This is a powerful learning tool. This book is absolutely essential for anyone who wants to understand Chaos Theory and Fractal geometry. It is very highly recommended.

  4. 4 out of 5

    Ken Sharp

    The authors of this book tried to take a branch of math and make it approachable for non-math people. Mostly they were successful in that, although it's a little hard to keep people interested through a very dense, 900+ page book. Full disclosure: I didn't read the entire book word-for-word. I was mostly interested in the example programs at the end of each chapter. I took it upon myself to convert the BASIC code to javascript that can run in your browser. My results are here: http://sharpk60.blo The authors of this book tried to take a branch of math and make it approachable for non-math people. Mostly they were successful in that, although it's a little hard to keep people interested through a very dense, 900+ page book. Full disclosure: I didn't read the entire book word-for-word. I was mostly interested in the example programs at the end of each chapter. I took it upon myself to convert the BASIC code to javascript that can run in your browser. My results are here: http://sharpk60.blogspot.com/2015/11/...

  5. 4 out of 5

    Charles Frode

    Wow! Wanna understand chaos theory and fractals? Who doesn't? Seriously, this college level text is full of wonderfully succinct explanations about how life unfolds according (chaos) and the wonderful patterns or structures it leaves (fractals). Check out Feigenbaum's constant if you want to understand the evolution of everything. Seriously. Dense text, math, but it's worth the digging to get the jewels. Wow! Wanna understand chaos theory and fractals? Who doesn't? Seriously, this college level text is full of wonderfully succinct explanations about how life unfolds according (chaos) and the wonderful patterns or structures it leaves (fractals). Check out Feigenbaum's constant if you want to understand the evolution of everything. Seriously. Dense text, math, but it's worth the digging to get the jewels.

  6. 5 out of 5

    Andrew Davis

    A great introduction to fractals and chaos with amazingly simple mathematics, and accompanied by a number of great pictures. The authors put a lot of effort into ensuring a clear presentation, which in turn resulted in its size presenting some challenges. As both a text and reference source would make a great addition for anyone interested in those subjects.

  7. 4 out of 5

    Paige McLoughlin

    This is a book I read or skim or have varying levels of engagement with each time I pick it up. I always get something new from it. Fractals, Chaos, and Power laws started getting my attention in the late 80s in my deadhead days. The patterns created jived well with my psychedelic aesthetic at the time and I became intrigued by the subject and have had an eye out for books on it ever since.It seems nature quickly tired of the boring old geometry of Euclid (circles and triangles only take you so This is a book I read or skim or have varying levels of engagement with each time I pick it up. I always get something new from it. Fractals, Chaos, and Power laws started getting my attention in the late 80s in my deadhead days. The patterns created jived well with my psychedelic aesthetic at the time and I became intrigued by the subject and have had an eye out for books on it ever since.It seems nature quickly tired of the boring old geometry of Euclid (circles and triangles only take you so far) but an iteration of fleas being bitten by smaller fleas who in turn are bitten by smaller fleas and so on. The power of iteration seems to be a powerful form generator in nature and she uses it all the time. Using mixing as well another character that nature adores deterministic Chaos aka the butterfly effect where a system that starts with extremely close initial conditions soon diverges unpredictably. It is the reason why weather forecasting is pretty much useless extrapolating a week or two out into the future. And my favorite persona comes on stage the Mandelbrot another set of points that is created by a simple iteration process that generates infinite complexity and intricate beautiful patterns it is exhibit A for Plato's heavenly form. So little goes in to generate so much. Books like this get me to overcome my laziness and engage with the math. A well I draw upon often. 3 likes · Like ∙ flag following reviews READING PROGRESS December 24, 2020 – Started Reading December 24, 2020 – Shelved December 26, 2020 – page 14 1.62% "found the other big doorstop of a book I enjoy so much. Scribble scribble," December 26, 2020 – page 61 7.06% "intro examples in chapter one the Sierpinski gasket, The multiple copier machine copy, shrink, twist (repeat) nature does that a lot. The logistic iteration and deterministic chaos and butterfly effect and fun with Fibonacci's rabbit sequence and how it tends to the golden ratio. All the hits are in the first chapter." December 26, 2020 – page 104 12.04% "This is a perfect book for a voraciously curious but very undisciplined mind. Good stuff." December 26, 2020 – page 128 14.81% "This is cool I get new insights (incites) every time I read it," December 26, 2020 – page 163 18.87% "Math and nature love to iterate. We are all constructivists now." December 26, 2020 – page 192 22.22% "Hausdorf measures and measuring fractional dimensional freaks that seem to populate actual existing reality we have here." December 27, 2020 – page 192 22.22% "an empirical method of figuring out fractional dimensions in box-counting methods that work for objects in the real world presented to the observer." December 27, 2020 – page 214 24.77% December 27, 2020 – page 276 31.94% "going into the gory details of actually building fractals via specific iterative methods." December 27, 2020 – page 329 38.08% December 27, 2020 – page 329 38.08% December 27, 2020 – page 376 43.52% "space-filling curves" December 27, 2020 – page 433 50.12% "I love the Mandelbrot set so easy to generate simply points on the border between contained and escaping to infinity of complex numbers added and squared over and over again. The equation for people into that is C(n+1)= (C(n) + K)^2 over and over again. I will drop a video here. https://www.youtube.com/watch?v=NGMRB... https://www.youtube.com/watch?v=FFftm..." December 27, 2020 – page 433 50.12% "Randomizing fractals and power spectra with Brown, White, Pink, and Black noise. Fun stuff I am fascinated with the fact that there are different flavors of randomness that obey different distributions of statistical noisiness. I love when something that seems like one thing from far away turns out to be many things up close." December 27, 2020 – page 433 50.12% "Deterministic Chaos (Butterfly effect) and the mixing or folding analogy for how it comes about mathematically" December 27, 2020 – page 541 62.62% December 27, 2020 – page 541 62.62% "Period doubling as a route to chaos and Feigenbaum number that expresses the proportions to that doubling. Behold another video. https://www.youtube.com/watch?v=ovJcs..." December 27, 2020 – page 705 81.6% "the strange attractor which has chaotic orbits that neither repeat nor are predictable but stay in a certain range. The Lorentz attractor for example can be constructed from a handful of partial differential equations that can't be cleanly solved but makes just such a strange attractor that has chaotic orbits but in a certain well definite range in 3-dimensional space." December 27, 2020 – page 839 97.11% "Mandelbrot sets and their relation to Julia sets. They are connected and generated by very similar methods." December 27, 2020 – Shelved as: early-twenty-first-century December 27, 2020 – Shelved as: european-history December 27, 2020 – Shelved as: general-science December 27, 2020 – Shelved as: mathematics December 27, 2020 – Shelved as: philosophy December 27, 2020 – Shelved as: physics December 27, 2020 – Finished Reading January 17, 2021 – Shelved as: chemistry January 17, 2021 – Shelved as: college-textbook January 17, 2021 – Shelved as: computer-science January 17, 2021 – Shelved as: engineering January 17, 2021 – Shelved as: late-twentieth-century

  8. 4 out of 5

    Krishna

    This was my first introduction to the theory of chaos and non linear dynamics. Provides a comprehensive approach to understanding chaos in many natural phenonomena happening around us, while keeping the reader interested

  9. 5 out of 5

    Asgar

    Very hard read. To be honest, I'm only two-thirds a way through it. I'm keeping more as a reference book, which is what it's meant to be for in the first place... Very hard read. To be honest, I'm only two-thirds a way through it. I'm keeping more as a reference book, which is what it's meant to be for in the first place...

  10. 5 out of 5

    Oren

    science hurts.

  11. 5 out of 5

    Tex Kaplan

    Beautifully written and illustrated with tons of cool stuff. Discusses many topics which can be explored independently.

  12. 4 out of 5

    Ron Banister

    Tough to read but worth the effort!!

  13. 5 out of 5

    Luke

  14. 4 out of 5

    Piet de Roo

  15. 4 out of 5

    Cesar Gonzalez-Perez

  16. 5 out of 5

    Alejandro Pulver

  17. 4 out of 5

    aroundinteger

  18. 5 out of 5

    Diana

  19. 4 out of 5

    Sleeping with Ghosts

  20. 4 out of 5

    Anna Budzik

  21. 4 out of 5

    Oliver

  22. 5 out of 5

    Daniel

  23. 5 out of 5

    Cheryl Barton

  24. 4 out of 5

    Jeff

  25. 5 out of 5

    Simon

  26. 5 out of 5

    Vic Dillahay

  27. 4 out of 5

    Vb

  28. 5 out of 5

    Aml

  29. 4 out of 5

    M Hameed

  30. 4 out of 5

    Dragon Adithya

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