This section analyses the nature of the interface between finite and infinite, 'spiritual' and physical, as revealed by the deeper fractal nature of life.
[Excerpt Be and Become, © ProCreative, Sydney 2000]
We can reasonably expect that if the whole-as-the-part model is universal, we will see the model universally apparent in nature.
That is to say, we should expect that the inseparable-duality of the Finite within the Infinite is also readily observable. We should be able to “see” the boundary between the physical and the 'spiritual.'
Perhaps in an analogous sense to those “magic eye” 3-D pictures, we might expect that as we look more closely at the world we will see this inseparable duality.
With the discovery of fractal geometry (the Mandelbrot Set), we have one method by which to recognize how the transition to thingness (physical reality) from no-thingness from whence it comes, occurs.
The Mandelbrot Set (and the general field of fractal geometry) could be considered to be the mathematician’s holographic model of the physical within the spiritual (infinite). For within any section of the Mandelbrot Set’s boundary lies, literally, infinite depth of detail, with each succeeding layer being a holographic model of the former.
Fractals represent the 'latticework' along which and within which the complex forms of nature naturally incline or unfold. As potentials and possibilities congeal into actuality, the solidification proceeds along certain lines of probabilities, all based on fractal geometry. Remember that individuality allows uncertain, irregular actualization, so fractal geometry is more representative of group behavior rather than individual behavior.
The geometric patterns given form by fractal geometry intimately imitate many complex forms in nature including inanimate objects, flora and fauna. In other words, fractal geometry can be thought of as the draftsmen’s drawings or blueprints by which nature in its infinite complexity seems to construct itself. And these draftsmen’s drawings are all variants of the one simple formula which maps the interface between the infinite and the finite. As James Gleick observed 'At the boundary life blossoms.'
Fractal geometry helps map or chart the process of solidification of 'infiniteness' into localized matter and energy - in effect, fractal geometry maps the interface between the 'spiritual' and the physical.
Fractal geometry can be used to create images which mimic the images of nature, some examples of which include trees, fern leaves (Figure 6.1), cliffs, capillary beds and entire mountain ranges complete with snow capped peaks.
"Once you develop a fractal geometer’s eye you can’t but help see them everywhere."1
John Briggs similarly noted that
"Trees and plants can be simulated by recursive programs which contain instructions for drawing repeated shapes to create twigs, stems, leaves and flowers, while randomly rotating them or bending them, and changing their thickness after a certain number of iterations. By carefully adjusting parameters and randomness, Przemyslaw Prusinkiewicz of the University of Calgary, Canada, has been able to generate imitations of specific botanical forms, such as the plant Mycelis Muralis."2
Professor Ian Stewart of the Mathematics Institute, University of Warwick noted that with the aid of fractal geometry:
“You see islands of order in a sea of chaos.”3
Scientists are finding that the entire universe is one large fractal. As Francesco Sylos Labini, an astronomer at the University of Geneva, suggested
"... studies we have done show that the distribution of matter is fractal, just like a tree or a cloud. ... our tests show that the Universe never becomes homogeneous in the available galaxy samples. It remains hierarchically clustered. It remains fractal."4