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Fractals - Patterns and Chaos

Posted: October 17th, 2010, 11:17 am
by ExSan
A Journey in The Mandelbrot setBenoît Mandelbrot 1924-2010

Fractals - Patterns and Chaos

Posted: October 18th, 2010, 10:14 am
by ExSan
BBC - In Pictures Mandelbrot Fractals

Fractals - Patterns and Chaos

Posted: October 18th, 2010, 12:06 pm
by Traden4Alpha
QuoteOriginally posted by: outrunWhy are the colours not symmetrical (horizontal mirror) in this one?Curious!It's not the phase angle of the gradient.My guess is that its something related to MOD(X,Y)

Fractals - Patterns and Chaos

Posted: October 18th, 2010, 12:23 pm
by Traden4Alpha
WHOA! That's too freaky!It's good evidence of the Feigenbaum constant.

Fractals - Patterns and Chaos

Posted: October 18th, 2010, 12:37 pm
by ExSan
QuoteOriginally posted by: outrunT4A, I was looking for various coloring scheme's to figure this our, ..when I found this, !! Did you know?where ? where ? woul like to see the theory behind the graph.

Fractals - Patterns and Chaos

Posted: October 18th, 2010, 12:43 pm
by Traden4Alpha

Fractals - Patterns and Chaos

Posted: October 18th, 2010, 8:52 pm
by ExSan
NS - The Chaos Theory Of EvolutionQuoteForget finding the laws of evolution. The history of life is just one damn thing after another---------------------------The link between environmental change and evolutionary change is weak - not what Darwinists might have predicted---------------------------Iterating these unpredictable changes over hundreds or thousands of generations will inevitably lead to evolutionary changes in addition to any that come about by the preferential survival of certain phenotypes. It follows that macroevolution may, over the longer-term, be driven largely by internally generated genetic change, not adaptation to a changing environment.---------------------------The evolution of life has many characteristics that are typical of non-linear systems.First, it is deterministic: changes in one part of the system, such as the mutation of a DNA base, directly cause other changes. However, the change is unpredictable. Just like the weather, changes are inexorable but can only be followed with the benefit of hindsight.Second, behaviour of the system is sensitive to initial conditions. We see this in responses to glaciations in the Quaternary period. The exact circumstances of the beginning of each interglacial determine the development of the whole period, leading to unpredictable differences between interglacials (Quaternary Science Reviews, vol 14, p 967).Third, the history of life is fractal. Take away the labelling from any portion of the tree of life and we cannot tell at which scale we are looking (see diagram). This self-similarity also indicates that evolutionary change is a process of continual splitting of the branches of the tree.Fourth, we cannot rewind, as Stephen Jay Gould argued in Wonderful Life. Were we to turn the evolutionary clock back to any point in the past, and let it run again, the outcome would be different. As in weather systems, the initial conditions can never be specified to sufficient precision to prevent divergence of subsequent trajectories.

Fractals - Patterns and Chaos

Posted: October 26th, 2010, 2:20 pm
by ExSan
Code posted on Mon Aug 09, 10 05:43 PMusing the same function / algorithm; I have added the next instruction net->draw_circuference_centered_in_the_middle_of_AB_(...); AB - Line Segmentvoila les graphs: From the Downloadable File extract program ExSan_Petrie_Graph_II to your desktop and execute