A fractal zoom on a mandelbrot set, finishing on a dendrite area. Made using XaoS (freeware program) Music: Aalborg Fantasy Soundtracks - Timefreeze (free on Audioswap)
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www.ted.com At TED2010, mathematics legend Benoit Mandelbrot develops a theme he first discussed at TED in 1984 -- the extreme complexity of roughness, and the way that fractal math can find order within patterns that seem unknowably complicated.TEDTalks is a daily video podcast of the best talks and performances from the TED Conference, where the world's leading thinkers and doers give the talk of their lives in 18 minutes. Featured speakers have included Al Gore on climate change, Philippe Starck on design, Jill Bolte Taylor on observing her own stroke, Nicholas Negroponte on One Laptop per Child, Jane Goodall on chimpanzees, Bill Gates on malaria and mosquitoes, Pattie Maes on the "Sixth Sense" wearable tech, and "Lost" producer JJ Abrams on the allure of mystery. TED stands for Technology, Entertainment, Design, and TEDTalks cover these topics as well as science, business, development and the arts. Closed captions and translated subtitles in a variety of languages are now available on TED.com, at http Watch a highlight reel of the Top 10 TEDTalks at www.ted.com
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Music is "Research Lab" by Dark Flow ( www.myspace.com ) Read more geeky details and download the full-resolution video at fractaljourney.blogspot.com Details The final magnification is 2.1x10^275 (or 2^915). I believe that this is the deepest zoom animation of the Mandelbrot set produced to date (January 2010). Each frame was individually rendered at 640x480 resolution and strung together at 30 frames per second. No frame interpolation was used. All images were lovingly rendered by 12 CPU cores running 24/7 for 6 months. Self-similarity (mini-brots) can be seen at 1:16, 2:30, and at the end 5:00.
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A music video for Jonathan Coulton's song Mandelbrot Set by Pisut Wisessing made in Film 324: Cornell Summer Animation Workshop, taught by animator Lynn Tomlinson every summer for Cornell's summer session, in the department of Theatre, Film & Dance.
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This video shows you how the Mandelbrot set is generated, and what it means. Knowledge from my previous videos is assumed. You should at least watch the video just before this one, on Julia sets. Fractal Extreme: www.cygnus-software.com
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This is an extremely deep dive into the Mandelbrot set, to 2^316 (binary). In decimal that's 1E+95, or 1 with 95 zeros after it. The coordinates are identical to a similar deep zoom movie posted to YouTube by user metafis, but my version has higher resolution (648x480), and was rendered with 2x antialiasing (four pixels computed for every output pixel). It also has an improved palette, similar to the one used by the Wikipedia Mandelbrot page. The uncompressed video looks better of course--fractals are close to the worst case for video compression--but H.264 does surprisingly well. The video was rendered using my own fractal software, called Fractice, which supports distributed processing using a client/server architecture. The render took five months, using a cluster of up to 20 dual-core PCs on a LAN, all running the Fractice rendering server. The actual number of servers varied over the five-month period but averaged around 15. Rendering only occurred at night. Fractice is a free, open-source fractal explorer/renderer for XP/Vista. It supports navigation, history thumbnails, previews, antialiasing, deep zoom, printing, posters, palettes, multicore and distributed processing, movie recording, undo/redo, color cycling, and job control. It also has VJ features, such as mixing, mirroring, origin motion, palette tweening, dual-monitor, and MIDI. For more info and to download Fractice: fractice.sourceforge.net
A slow deep zoom into the Mandelbrot set, generated by FractalNet, my distributed fractal renderer. The original 1920x1080 HD version of this video required a total of 90459 billion iterations (an average of 26.8 billion iterations per frame). It took 12 days 1 hour 17 minutes to render on my 2.4GHz iMac. Watch this video in HD on Vimeo at www.vimeo.com More videos and hundreds of images available at michael-hogg.co.uk
By Jonathan Coulton. Made to show my Geometry class what I will cover in our fractal section at Simpson University. Mandelbrot zooms, Peano/Koch Curves, simple IFSs, fractal music, 3d Julia Set, Sierpinski Gasket, etc.
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Benoit Mandelbrot (Yale University, USA), "The nature of roughness in mathematics, science and art," Special Lecture, ICM 2006, Madrid, 27 Aug 2006. From the IMU website www.mathunion.org www.mathunion.org www.mathunion.org
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You may not know it, but fractals, like the air you breathe, are all around you. Their irregular, repeating shapes are found in cloud formations and tree limbs, in stalks of broccoli and craggy mountain ranges, even in the rhythm of the human heart. In this film, NOVA takes viewers on a fascinating quest with a group of maverick mathematicians determined to decipher the rules that govern fractal geometry. For centuries, fractal-like irregular shapes were considered beyond the boundaries of mathematical understanding. Now, mathematicians have finally begun mapping this uncharted territory. Their remarkable findings are deepening our understanding of nature and stimulating a new wave of scientific, medical, and artistic innovation stretching from the ecology of the rain forest to fashion design. The documentary highlights a host of filmmakers, fashion designers, physicians, and researchers who are using fractal geometry to innovate and inspire. www.pbs.org
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A mesmerizing, elegant, and deep journey into the Mandelbrot set . This is the full 3 minute version of the fractal animation from the music documentary "BACH & friends." Michael Lawrence's beautiful film features some of the world's greatest musicians performing and reflecting on the genius of Bach: www.mlfilms.com There is a poetic connection between the music of Bach and the famous fractal known as the Mandelbrot set. Bach's compositions represented the height of Baroque sensibilities; intricacy, nested levels of adornment, and the suggestion of infinite space were compelling structural properties in the art and architecture of his day. Fans of Bach often refer to a sense of endless spirals or wave-like circles-within-circles. Such descriptions are reminiscent of the infinite, Baroque-like detail of the Mandelbrot set. It is striking to see how the sense of motion we experience in this fractal zoom presents a perfect counterpoint to the unfolding of Bach's Contrapunctus IX. This animation was featured at the 2010 Bridges Short Movie Festival. -HB Produced by Harlan Brothers: www.brotherstechnology.com .
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An epic journey across the Mandelbrot set, exploring many different embedded Julia sets. Please watch this video fullscreen in 720p HD. Designed and rendered using FractalNet, my distributed fractal renderer. STATS FOR THIS VIDEO Total iterations: 104066 billion Average iterations per frame: 6.69 billion Render time: 14 days 13 hours 6 minutes Average render time per frame: 1 minute 21 seconds Average rendering rate: 82.8 million iterations/second Deepest zoom: 400 billion times magnification (2.5E-12 view width) LINKS Watch this video in HD on Vimeo at: vimeo.com More info, videos and images available at: michael-hogg.co.uk Wikipedia article: en.wikipedia.org .
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Arthur C. Clarke presents this unusual documentary on the mathematical discovery of the Mandelbrot Set (M-Set) in the visually spectacular world of fractal geometry. This show relates the science of the M-Set to nature in a way that seems to identify the hand of God in the design of the universe itself. Dr. Mandelbrot in 1980 discovered the infinitely complex geometrical shape called the Mandelbrot Set using a very simple equation with computers and graphics. ------------------------------------------------------- Springer Science + Business Media, LLC www.springer.com
The M-Set is so interesting although I have no idea as to the mathematics side of it, what I do know is, that it proves a massive principal - that chaos can come from a set or defined parameter! ie The posibility of an unlimited imagination and 'free will' emerging from the limited or set parameters of a brain. The Mandelbrot Set is one reasonably simple equation that plots a point on a graph and then another point in relation to the first. That's all. Yet it creates an endless and truly chaotic result. Now think of the complex system of electrical and chemical equations that must be present in the brain (the brains M-Set equation so to speak) and consider the possibilities for the type of graph (thoughts) or even true free will that it might create. It's sort of a scary thought to me but it means that true free will is no longer only explained by something outside of the bio-mechanical functions of the body. Before this concept the argument said that if we were only mechanical and had no soul or spirit, then we only had a feeling or illusion of free will. Now one's able to argue that free will is possible from the set parameters of a bio-mechanical brain/body. Hope this rocks your world like it did mine. Enjoy the mysteries of defined infinity!
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Sonification of the Mandelbrot set fractal. Composed by Gustavo Díaz-Jerez. Procedure: - X axis of image mapped to time, in seconds. - Y axis of image mapped to frequency (27.5 - 4163Hz, continuous, exponential scale, using sinusoids). - Brightness of image mapped to dynamic range. Black (0,0,0) = silence (-INF dB). White (255255255) = Max (0 dB) The right side shows a spectrogram and a bar diagram of the sound. The bottom shows the wave form. Postprocessing: bass frequencies boost. Notice that this is not somehow inspired or "based" on the image. It IS how the image translates to sound for the given paramenters. More information and sheet music available at www.fractalmusicpress.net http
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Mandelbrot set (outlined in red) with Pickover stalks (green and purple). Rendered on my GPU using a pixel shader, runs in realtime with a reasonable resolution.
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(creator's note: I am disappointed with youtube's compression quality of my video despite uploading a lossless 720p source video) The title is a reference to Siddhartha Gautama who meditated intensely under a bodhi tree until he achieved enlightenment and became the Buddha. I seek enlightenment through art and science and my work with fractals. About one year ago I decided to refresh my rusty C++ programming skills by writing a little program to draw Mandelbrot fractals - something that has always interested me. In doing a little reading into it I discovered the so called "buddhabrot" method of rendering Mandelbrot fractals which consists of mapping out orbits (all of the in-between values created during calculation) rather than simply coloring pixels based on the final count of calculation loops. This essentially shows you the "Z" plane of the Mandelbrot set. The typical rendering method shows you the C (constant plane.) Z and C of course come from the well known equation Z = Z^2 + C. If you consider Z and C as planes, each having a real and imaginary axis, then the Mandelbrot set can be viewed as a 4-dimensional object. This can be rotated and viewed from different perspective and planes which this animation does. I was hooked on this style of fractal from the moment I rendered my first image. I wanted to see more, so I tried to render a higher resolution version and that's when I hit the wall that I feel has prevented this fractal from being fully explored and <b>...</b>
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www.hd-fractals.com Originally posted on www.vimeo.com Here is a nice deep zoom into the Mandelbrot set. The words "nice" and "deep" fall a bit short actually. "Mathematical Porn" is a better description. After watching this video things in my room started to bend and breathe!! I hope you enjoy the trip!! The final magnification is e.214. Want some perspective? a magnification of e.12 would increase the size of a particle to the same as the earths orbit! e.21 would make a particle look the same size as the milky way and e.42 would be equal to the universe. This zoom smashes all of them all away. If you were "actually" traveling into the fractal your speed would be faster than the speed of light. You might like to know that this animation took me about two days to set up. My computer then rendered day and night non-stop for just over a month to produce the animation. The resulting twenty-eight anti-aliased 1280x720 AVI files (each just under 2GB) were each watermarked at full frames (uncompressed) Then I stitched them all together uncompressed. I also added the audio track at the same time. This was all done in Virtual dub. (except watermarking) The final watermarked Avi with audio is a whopping 46GB - Then I compressed it to 495mb so I could upload it onto vimeo. I think it still looks fairly crisp.. BY TEAMFRESH www.hd-fractals.com
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For a description of the annotations, see below: What is a Mandelbrot zoom blooper? It's what happens when you commit 6 months of computing time on three computers to create something that doesn't turn out the way you expect! The color rotations that begin at 1:36 were unintentional. However, the side effect is that the animation is much more psychedelic than expected due to the color cycling and also brings out details that are not apparent with still images. Annotations: This animation shows patterns that only a zoom animation reveals - patterns that still images do not convey. For example, note how the "branches" rotate clockwise and counter-clockwise. Furthermore, note how the clockwise rotations double from 2 arms, to 4, to 8, and so on. And note how the counter-clockwise arms also double, although starting from 10. Annotations counting these branches for the first zoom series starts at 0:53. Thanks to Dark Flow for the music. For more geeky details, go to fractaljourney.blogspot.com .
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This is what happens when you play with numbers too much. Mandelbroth's fractal geometry set is nothing to mess with, especially by old guys with computers.
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Fractal Zoom !deep! take a mellow deep & chilled trip with teamfresh and 90watts.com
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This is a rather deep zoom. A bit into it you can also see one of Julia Sets (lookalike i presume) inside the Mandelbrot set. Rendering time for this would be nearly 8000 hours on a 1 GHz Athlon Thunderbird. (But of course, not rendered on a sigle CPU.) Music is Nangilima from the album Nangilima by Doc. Coordinates for anyone to test with their favourite program is: Real: -0.1049366816451579879883700925833001280734371117572419840344588951672691089064778 Imag: 0.9276043254180429357601469594238546238042126160969261398796450536437845581500922
When we participated in the 2008 Ig Nobel Price Ceremony (improbable.com we had the pleasure of meeting noted mathematician Benoit Mandelbrot. Unfortunately, our good friend Jonathan Coulton (www.jonathancoulton.com), author of the song "Mandelbrot Set", was not there with us. Luckily, we had our video camera with us...
What is a 'fractal' and how does it work?
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Hi, I made this using the "TetraBrot Explorer" Java applet, made available to me by the guys at www.3dfractals.com, thanks guys. Higher quality vids, or screen shots, are available upon request, send me a youtube message w email address. Sorry for not having any audio track, I recommend listening to minimal/tech house, try: www.juno.co.uk
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Music is by c418, "love" from the album circles. c418.org http - map download This is what it looks like when you import a mandelbrot fractal into Omen as a heightmap. Pretty neat, but made my client crash quite a bit, and because I did multiple recordings the music skips as wel, for some reason. Oh well. The map was imported into Alpha (from Omen) using MCEdit.
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Lecture Series on Chaos, Fractals and Dynamical Systems by Prof.S.Banerjee,Department of Electrical Engineering, IIT Kharagpur. For more details on NPTEL visit nptel.iitm.ac.in.
More about this programme: www.bbc.co.uk Chaos theory has a bad name, conjuring up images of unpredictable weather, economic crashes and science gone wrong. But there is a fascinating and hidden side to Chaos, one that scientists are only now beginning to understand. It turns out that chaos theory answers a question that mankind has asked for millennia - how did we get here?
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