Mandelbrot Set

This video is a collective zoom on the Mandelbrot set. The Mandelbrot set, named after Benoit Mandelbrot, is a set of points in the complex plane, the boundary of which forms a fractal. Mathematically, the Mandelbrot set can be defined as the set of complex c-values for which the orbit of 0 under iteration of the complex quadratic polynomial (xsub n+1)=(xsubn)^2+c remains bounded. That is, a complex number, c, is in the Mandelbrot set if, when starting with xo=0 and applying the iteration repeatedly, the absolute value of xsubn never exceeds a particular number (that of which depends on c) for however large n gets. When graphed on a complex plane, the set is seen to have an elaborate boundary which does not simplify at any given magnification, making the boundary a fractal.
The mere visual depiction of this video is absolutely astonishing to me. I find it amazing that one can just zoom in indefinitely onto a design. I chose to post this video because the concept of fractal art is an application of an infinite complexity creating disordered order, an important concept in this course.

Posted at 03:42AM Oct 12, 2008 by Daniel Evan Piephoff in MediaHunt2  |  Comments[0]

Mandelbrot Set Spiral Zoom

"linktext":http://www.youtube.com/watch?v=pMGo7jFH-A8 This video zooms in on the mandelbrot set continuously. It zooms in on part of the fractal that spirals, but each line in the spiral has new spirals inside. When we zoomed in on the mandelbrot set in class we didn't look at any area that spiraled this way. This shows how many different characteristics are included in the mandelbrot set. Any area you zoom in on shows more detail.

Posted at 09:08PM Oct 07, 2008 by Samantha Baughman in MediaHunt2  |  Comments[0]

Fractals and Plants

Fractals are not only mathematical abstraction, which can be used for creation of abstract or realistic images. They can be found in our world in various plants. Below you can see several examples of fractals in nature.

The most known fractal is fern leaf. Every little leaf of fern repeats whole large leaf.


Another interesting nature fractal is romanesco cauliflower, which is a cross between broccoli and Cauliflower, which accentuates the great fractal spiral patterns on the top.

Posted at 06:51PM Oct 07, 2008 by Karin Hurwitz in MediaHunt2  |  Comments[0]

Tree-Making Rules

Link: http://www.youtube.com/watch?v=ZVyi4ykVHJM

This video shows a virtual tree being created through a program called L-konna that is used to make 2D and 3D plants. This video reminded me of the section on tree branches from the Self-Made Tapestry. The reading included sets of rules created by Roux and Honda to describe how tree branches are formed. After following the link that accompanied the video, I found the code representing the rules for this tree in the L-konna program. By looking at both the tree itself and the code, it is obvious that these rules are a bit more complex than the rules from the Self-Made Tapestry, especially with the introduction of color to the system. Nevertheless, the resulting tree is a clear representation of a fractal, exhibiting branching and self-similarity.

Posted at 03:16PM Oct 07, 2008 by Nathan Combs in MediaHunt2  |  Comments[0]

Fractals in Africa: Religious Applications

This is an interesting little research project, funded by the Fulbright Grant, for researcher Ron Eglash who looked at overhead photos of tribal African villages and saw fractals in the construction. So he went to Africa and discovered that fractals occurred in structures because the local religion was based on a kind of fractal pattern, with families and villages displaying self-similar behavior. He says at one point that, some of the fractals designed are intuitive while others are based on highly developed algorithms, where pieces are separated even by age groups, and are built recursively. There are references in the video to log log plots that reveal incredibly cost beneficial fences, built from reeds with a fractal pattern to prevent wind and dust from getting through the fence, There is also a reference to a religious algorithm that uses deterministic chaos in divination. Although the video is rather long, the topic is interesting and the speaker is engaging: truly worth watching.

http://www.youtube.com/watch?v=7n36qV4Lk94

Posted at 10:11AM Oct 07, 2008 by Garik Cruise Sadovy in MediaHunt2  |  Comments[0]

Biological Fractal

The biological world has always been fascinating to me.  An example of its extrodinary complexity is evident in the above picture.  You can see the branches of a bacteria colony curving outward from the central origin, giving way to even smaller branches and so on.  The structure is fairly dense, so I would imagine it would have a large fractal dimension.  Also, the self-similarity of the branches is very deep, especially for a biological fracal, where tree's and plants may have 5 repeating branch depths.

Posted at 07:24AM Oct 07, 2008 by William Stoy in MediaHunt2  |  Comments[0]

Lightning (In all its glory!)

Lightning Storm

Lightning Video

Lightning has always sparked my interest. I do not know if it is because I grew up in a place where lightning continually strikes near my house, or because they are very electrifying. In the clips you can see the fractal formations in lightning. The first is more or less of a slide show. However, since the camera is centered on one location, it is easy to see the different branching of lightning. You can see that none of the lightning strikes will appear like the ones before. Lightning in my opinion is nature's most spontaneous, unpredictable, and powerful force.

Posted at 07:17AM Oct 07, 2008 by Detric Robinson in MediaHunt2  |  Comments[0]

Out of this world fractals

This may not be the best example, but this view of Jupiter shows the gas giant with a somewhat fractal-like surface. The weather patterns on it's surface have a repeating pattern, especially so in the band near the middle left of the image. In addition to the bands, there is a pattern of the small round spirals. I'm sure that even our (Earth's) weather patterns show a fractal nature, but this photograph shows a pattern that is much easier to see due to Jupiter's milky atmosphere.

Posted at 09:25PM Oct 06, 2008 by Eric Harrell in MediaHunt2  |  Comments[0]

Mandelbrot Fractal Zoom

http://www.youtube.com/watch?v=ggy1Tf3dquY&feature=related http://www.youtube.com/watch?v=-rooASiucI4&feature=related These videos both display the self symmetry of Mandelbrot sets. As one magnifies the Mandelbrot sets, one will see repeating clusters that are exactly the same as the original region. These Mandelbrot sets are said to look like "malformed Russian dolls" that continuously get smaller but they all look the same as the entire Mandelbrot.

Posted at 04:11PM Oct 06, 2008 by Brooke bernard in MediaHunt2  |  Comments[0]

Fractal tree simulator

The link to the simulator is http://www.vestaldesign.com/design/tree-simulator/ .

This website randomly creates a different fractal tree each time you plant a seed or click in the window. You will notice that all of the trees have a similar pattern, but between multiple trees there are distinct differences. A very interesting feature in the simulation is the "wind" that is present, and watching how it affects the differently shaped trees.

A note: for me to view the simulation I needed to install a java plugin, and the application is also very computationally intensive, so just be aware of that.

Posted at 04:03PM Oct 06, 2008 by Timothy Michael Dannenhoffer in MediaHunt2  |  Comments[0]

Fractals and Art

Fractals often seem almost intrinsically fascinating, sometimes even beautiful.  Doubtlessly, this contributed to their migration out from the realm of mathematics and into the minds of the rest of the world, including artists.  John (a photographer) presented the two photos seen here during this interview.  The right most photo, captioned 'photography and fractal math' has obviously been manipulated to demonstrate fractal properties.  But why is it so captivating?  We often see fractal forms in nature, and so we might simply be used to associating them with nature's beauty.  They resemble the intricacies of the natural world that most of us share a common reverence for.  The left picture, for example, made simply through infrared photography, seems to hold just as much a fractal nature as the picture on the right.  This one, however wasn't manipulated, it simply captures the fractal aspects of nature; it is just beautiful.  

Posted at 09:15AM Oct 06, 2008 by Jeffrey Fowler in MediaHunt2  |  Comments[0]

Similarities in Morphologies

In the reading, Phillip Ball explains how Hele-Shaw cell situations-- while still exhibiting a form of Laplacian growth-- tend to create fat-finger branches instead of wispy tendrils.  This pattern, caused by surface tension's area-reducing properties, is called the "dense-branching morphology".

Simulating coarsening dynamics of fractal clusters

This video shows a process with a similar morphology to the results of the Hele-Shaw experiments.  It illustrates the dynamics of coarsening through surface tension of a diffusion-- limited aggregate as described by the Cahn-Hilliard equation.  As one can see, the aggregate begins by displaying the thin branching pattern of viscous fingering, but then widens and grows into one resembling a dense branching morphology.  The purpose of this video is to support the argument that a Hele-Shaw model belongs to the same universality class as the Cahn-Hilliard equation.

Posted at 01:08AM Oct 06, 2008 by Mary Burroughs in MediaHunt2  |  Comments[1]

Fractals in nature

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This video is called "Eye Candy" for its various pictures of fractals in nature, and it definitely lives up to its name.  There are a lot of great examples of vivid fractals, which can be defined loosely as objects that can be viewed in smaller or different sections of the same object and appear to be similar, or self-similar.  Some of the coolest and best examples are the tiger at 1:11, the flower at 1:19, the water "sections" at 1:44, and the eel at 3:11.  All of the above demonstrate self-similarity as they could be broken down to show similarities within themselves.

http://www.youtube.com/watch?v=BdqXhV1cEd8

Posted at 12:33AM Oct 06, 2008 by Jacob Brennan in MediaHunt2  |  Comments[0]

Koch Snowflake

http://www.youtube.com/watch?v=1vzZoZrgraU This is a video of a 3d version of a Koch Snowflake. As the video progresses the figure continues to grow, producing more and more triangles until it reaches its capacity, which is a cubed figure. The one problem that i have with this video is that unlike in the Koch Snowflake, the existing pyramids grow in size as new ones appear. Anyway it is still a pretty cool video.

Posted at 10:15PM Oct 05, 2008 by thomas stuart mccawley in MediaHunt2  |  Comments[1]

Chaos and Fractals

http://www.youtube.com/watch?v=V9F48Luw91I

Chaos is a theory, a theory that seems to shed light on many of the questions unanswerable by linear equations and the mathematical ideas that come with that. If one looks closely, fractals are very much a part of chaos. Fractals are always self-similar, and most seem to be deterministic, following rules for their patterns. They can be seen in the Julia and Mandelbrot sets; they can be seen in mineral dendrites and snowflakes. Chaos is a theory; fractals are the shapes caused by the mathematics of chaos.

Posted at 07:01PM Oct 05, 2008 by Asia Murphy in MediaHunt2  |  Comments[0]