ABSTRACT PAINTINGS

This abstract image is actually the surface of a glass of Coke with ice cubes. I shot it with a digital camera while on an airline flight. The picture was then digitally modified. I know it technically belongs as a photograph, but the floral feel looks more like paint than a digitized glass of Coke, so here it is.

Based on the number phi, the fibonacci series and the golden ratio.

The following are probably more properly classified as 'photographs'  although they have been 'hand-colored.'  These 'places' are  found inside various fractal equations.  Since both the Mandelbrot and Julia sets are defined by the complex function z = z^2 + c, the Mandelbrot-Julia manifold might be visualized as a four dimensional object.  A given planar slice of that object yields the familiar Mandelbrot set and for each point of that set, a perpendicular slice would yield the Julia set for that point.  Some of the following objects were created using planes that are neither "Julia" nor "Mandelbrot" but help create the distortions that recreate familiar patterns.  I have attached the central coordinates of each image -- two for Mandelbrot objects and four where more exotic slices were used.

  South Pacific:  A springtime aerial photo of a cluster of islands in full bloom.  Re(c) = -1.088768656; Im(c) = 0.31120674; Re(Z) = 0.0247312134; Im(z) = 0; mag = 1

  Winter Window:  Ice crystals on a window pane.  Re(c) = -1.2141114812111; Im(c) = 0.1661321748978; mag = 51776

  Protostar:  An infant star emerging from a glowing swirl of incandescent dust.  Re(c) = -0.8361129760742; Im(c) = 0.2229213714599; mag = 190

  Fire Lace:  Re(c) = -0.927263903; Im(c) = 0.295278898; Re(Z) = -0.004956357; Im(z) = 0; mag = 1

  Clouds on Fire:  A western sunset over a beach.  Re(c) = -.952255241; Im(c) = 0.261192233; Re(Z) = -0.544828052; Im(z) = 0.253280521; mag = 1

  Carrollian Wormholes:  OK, we haven't seen such things in nature yet, but we haven't ventured forth very far either.  For some reason, I always think of Alice in Wonderland when seeing such fractal images.  Here I exaggerated that sense with the Cheshire Cat-like painting of the image.  Re(c) = -0.0829661488533; Im(c) = 0.2132500708103; mag = 726

  Fractal Galaxy:  Perhaps not too distant from the Milky Way.  Re(c) = -0.907228972; Im(c) = 0.255827296; mag = 112

  Lava Flow:  The glowing lava sliding down a volcanic slope.  Re(c) = 0.292568684; Im(c) = 0.592022395; Re(Z) = -0.170587835; Im(z) = 0.199419093; mag = 1

The following fractals do not use "exotic slices" of the Mandelbrot set but are selected from a wide range of functions using Fractal Explorer.