Reflective
Spheres of Infinity: Wada Basin Fractals
(In physical reality and digital visualization)
Perhaps
the Best Example
of a very rich and interesting natural fractal
is the infinite series of interreflections when mirrored
spheres
(such as christmas ornaments) are packed together.
It may also illuminate properties of other processes
because the fractal is produced by perfect spheres
arranged into the most economical packing arrangement
used by nature and most waves
are actually spherical.
Simplest
SetUp for Wada Basin Fractal
Is a Tetrahedron of FOUR Reflective Spheres

Bottom Three Spheres 
This one is Somewhat
Monochrome. For a more highcontrast Fractal It's
advisable to use 4 Differently Colored Balls.

Close Up Image of Bottom Three Spheres,
Showing Primary Wada Fractal Pattern

There Is Some Difficulty In Getting
a PERFECT Photo of a Wada Basin
(because the ideal viewpoint is the center of four
tangent reflective spheres lit by a single point
source light  the camera has to to be small and
positioned somehow in the center without casting
a reflection into the fractal)

Look in the middle and we see a beautiful fractal vortex!
Wada Photo (left) with similarities to Mandelbrot Set (right) :
Here is a shot i found from a digital photography
"DCP Challenge" contest online  nice color
choices!
"Wada basins are certain special basins of attraction studied in the mathematics of nonlinear systems. A basin having the property that
every neighborhood of every point on the boundary of that basin intersects at least three basins is called a Wada basin, or said to have the
Wada property. Unlike the Lakes of Wada, Wada basins are often disconnected. An example of Wada basins is given by
the NewtonRaphson method applied to a cubic polynomial with distinct roots, such as x3 − 1:" from Wiki
(simple Wada fractal in 2 dimensions)
The 3 dimensional Wada Basin example below is from a cover story
in Scientific American 2002
Photography is limited by equipment
quality and grain of the film, WADA Basins of INFINITE
Depth and Detail
can be calculated & rendered Digitally by Ray Tracing
Programs (POVray & probably other programs)
that are used to simulates shapes and trace very accurate
simulations of the path light takes.
This also allows for the option of using color palettes
that highlight certain prosperities of the are being inspected.
Below:
Better focus and color control in Digital Wada Basins.
Gorgeously rendered Wada Basin in blues, gray, white,
yellow and black
This and the next 10 images are from the prolific work
of by
Paul
Bourke, Swinburne University AU
Below: Zoom on area in Wada
Fractal above ...
Below:
Nice Result With Rainbow Hues in the Wada Fractal
by
Paul
Bourke, Swinburne University AU
Below: Crisp Contrast
in the basic pattern
is achieved by using black and lowsaturation
hues. Spheres
arranged as six vertices of an octahedron
Image credit: Dave Matthews,
Mathematics Instructor Minnesota West Community and Technical
College
Below: Another interesting
display method
just showing the wada reflections and leaving the spheres
blank .... Next
3 by Paul Bourke, Swinburne University AU

Below:
Wada with the spheres at the eight vertices of
a cube
Image by
Dave Matthews, Mathematics
Instructor Minnesota West Community and Technical College
Another
Analog Photograph of a "Real" Wada Basin made
of Christmas Balls
