Fractals such as this Asplenium fern can be generated easily with computers by applying a few simple mathematical operations. This fractal and others like it were first generated by Michael Barnsley and his colleagues in the 1980’s at the Georgia Institute of Technology.
Fractals exhibit exceptional diversity and yet are united by several core principles, including self-similarity on multiple levels of scale, infinite detail and fractional dimension.
Even if you don’t know how to program a computer, you can generate the fractals in this presentation using a Microsoft Excel spreadsheet available at http://tinyurl.com/6vrxrfe
Fractals exhibit exceptional diversity and yet are united by several core principles, including self-similarity on multiple levels of scale, infinite detail and fractional dimension.
Even if you don’t know how to program a computer, you can generate the fractals in this presentation using a Microsoft Excel spreadsheet available at http://tinyurl.com/6vrxrfe
The Barnsley fern unlike the fractals we see in everyday life is a mathematical fractal, and as such it has infinite detail. If you magnify any one of the pinnules, you will find a complete Barnsley fern within that pinnule, provided that you have performed enough iterations. After 32000 iterations, each pinnule is beginning to exhibit the characteristic form of the whole.
We can create the entire structure by scaling, rotating and shifting its parts because the whole is recursively defined by its parts. Notice that in the fractal fern above, that each pinnule comprises the entire structure within it.
The Barnsley fern unlike the fractals we see in everyday life is a mathematical fractal, and as such it has infinite detail. If you magnify any one of the pinnules, you will find a complete Barnsley fern within that pinnule, provided that you have performed enough iterations. After 32000 iterations, each pinnule is beginning to exhibit the characteristic form of the whole.
The Siphonaptera based on "On Poetry: A Rhapsody".
Big fleas have little fleas,
Upon their backs to bite 'em,
And little fleas have lesser fleas,
and so, ad infinitum.
This simple children's poem has been an inspiration to fractal enthusiasts for at least a generation.
Big fleas have little fleas,
Upon their backs to bite 'em,
And little fleas have lesser fleas,
and so, ad infinitum.
This simple children's poem has been an inspiration to fractal enthusiasts for at least a generation.
