Clouds are not spheres
Mountains are not cones
Coastlines are not circles
Bark is not smooth
Nor does lightning travel in a straight line

- Benoît Mandelbrot, in his introduction to ‘The Fractal Geometry of Nature’

This fractal artwork was inspired by, and a tribute to, Benoît B. Mandelbrot. Benoît Mandelbrot is a Polish mathematician and is best known as the father of fractal geometry. In mathematics, the Mandelbrot set that is named after Benoît Mandelbrot, is a set of points in the complex plane, the boundary of which forms a fractal. In 1975, Mandelbrot coined the term fractal to describe these structures, and published his ideas in ‘Les objets fractals, forme, hasard et dimension’ (1975; an English translation ‘Fractals: Form, Chance and Dimension’ was published in 1977).

Mandelbrot has been called a visionary. His informal and passionate style of writing and his emphasis on visual and geometric intuition (supported by the inclusion of numerous illustrations) made The Fractal Geometry of Nature accessible to non-specialists. The book sparked widespread popular interest in fractals and contributed to chaos theory and other fields of science and mathematics.

He also emphasized the use of fractals as realistic and useful models of many “rough” phenomena in the real world. Natural fractals include the shapes of mountains, coastlines and river basins; the structures of plants, blood vessels and lungs; the clustering of galaxies; and Brownian motion. Fractals are found in human pursuits, such as music, painting, architecture, and stock market prices. Mandelbrot believed that fractals, far from being unnatural, were in many ways more intuitive and natural than the artificially smooth objects of traditional Euclidean geometry.

Every time you enjoy one of the countless beautiful fractal artworks you see, you can give appreciation and thanks to Benoît Mandelbrot as well as the fractal artist, as without his life’s work we would not be viewing them at all. You can learn more about both Benoît Mandelbrot and the Mandelbrot set at the Wiki links I have provided below. Many thanks to Wiki for some of the information I have presented above.

Benoît Mandelbrot

Mandelbrot set

This was created in Apophysis. The original is 4800 × 6000 pixels at 300 pixels per inch. The fractal that sits within the large square at the bottom of the artwork shows the basic Mandlebrot set fractal. The rest of the artwork was created with transformations that are subsets of the Mandlebrot set.

The fractal was created as a transparency, and then layered over a gradient background that was created in Photoshop. The fractal gradient was created with ApoMap, a gradient editor commonly used with Apophysis. All of the post processing was done in Photoshop.The actual fractal has not been post processed at all, and is exactly as it was rendered.

Because the original is so large and difficult to see over the internet, I have included a few detail cutaways below. The cutaways are at 33% of the full-size artwork.

Thank you, Benoît! ;)

I am an artist, a photographer, a writer, a musician, a composer, a craftsman, a designer, and a programmer. I have been recognized for various works in all of these areas over the last half century.

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  • Gramia97
    Gramia97about 6 years ago

    nice work on both

  • Thank you so much, Debbie!

    – ArtByDrew

  • CanDuCreations
    CanDuCreationsabout 6 years ago

    Beautiful, romantic, very well designed work with great happy colors

  • Thank you so much, Thea! The hardest part was getting that first square to render absolutely square so it would represent the Mandelbrot within correctly. Sometimes it is the simplest things that are the most complex… just as in life! LOL

    – ArtByDrew

  • Elaine  Manley
    Elaine Manleyabout 6 years ago
    lovey work and info .. I see the Mandelbrot in this piece
  • Thank you so much, Lu! There are mandlebrot sets along the inner edges of all the transforms except the hearts. I can only hope Benoît would like it as well!

    – ArtByDrew

  • KcranmerArt
    KcranmerArtabout 6 years ago

    I see you are still creating brilliant works drew and this is no exception…I can’t get over the boldness of these colors…seriously eye catching and gorgeous in everyway!

  • Kellie!!! So good to see you up and about! I hope everything went well last week! I will email you soon, but in the meantime… how about taking this time you have to take some new pics!! ( I know… nag, nag, nag) :)

    Big Hugz


    – ArtByDrew

  • Desirée Glanville
    Desirée Glanvilleabout 6 years ago

    welll done!!! so happy and cheery! :)

  • Thank you so much, Daisy!!

    – ArtByDrew

  • coppertrees
    coppertreesabout 6 years ago

  • WOW!!! Thank you so much, Vickie!!

    – ArtByDrew

  • zooreka
    zoorekaabout 6 years ago

    Neat work… very nice Drew!

  • Thank you so much, Zoo!!

    – ArtByDrew

  • Heloisa Castro
    Heloisa Castroabout 6 years ago

    brilliant job!

  • Thank you so much, Heloisa!

    – ArtByDrew

  • Rupert  Russell
    Rupert Russellover 5 years ago

    It would be nice if you were to add this to our new group Julias & Mandelbrots

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