clifford_a-_pickover_surfing_through_hyperspacebookfi-org

228 notes
Shades of gray indicate the mapping's rate of explosion. As is standard with Julia
sets, "divergence" is checked by testing whether Q goes beyond a certain threshold, T,
after many iterations. For Figure D.I, the mapping is iterated 100 times and the iteration
count, n, is stored when | Q| - T. The logarithm of the iteration counter, n, is then
mapped to intensity in the picture. (See my book Computers, Pattern, Chaos, and
Beauty for more information.) Figure D.I represents a 2-D slice of a 4-D quaternion
Julia set. The slice is in the (a a , a 2 ) plane at level (a t , a } ) - (0.05,0.05). The constant q =
(-0.745,0.113,0.01,0.01) and T = 2. The initial value of Q is (a a , a 2 , 0.05, 0.05),
where a a and a 2 correspond to the pixel position in a figure.
Appendix G
1. In the fourth dimension, is it possible that many new elements would exist and
we would be adding an entire dimension to the periodic table? Philosopher Ben Brown
believes that there would be many more elements. If we assume that carbon is the only
material capable of building life, in four dimensions there would be a greatly decreased
chance that the correct elements would come together to form biomolecules compared
to 3-D space—thereby slowing down evolutionary processes. The initial life-forms
would have virtually no competition, but would take much longer to come into being.
The odds of intelligent life evolving in a 4-D universe would be even slimmer. The
lower the dimension, the better the chance of evolving life because the chances are
greater for having the right elements present at the right time.
Four-dimensional beings may well take in oxygen and nutrients from their outer
surfaces. Ben Brown believes that a 4-D creature would have no lungs, and would be
insect-like. As background, consider that insects cannot grow very large because they
have no lungs. Certain insect species breathe through the body wall, by diffusion, but,
in general, insects' respiratory systems consist of a network of tubes, or tracheae, that
carry air throughout the body to smaller tubelets or tracheoles that all the organs of the
body are supplied with. In the tracheoles, the oxygen from the air diffuses into the
bloodstream, and carbon dioxide from the blood diffuses into the air. The exterior
openings of the tracheae are called spiracles. In four dimensions, a being's surface area
would be so much greater in proportion to its internal volume that body size would be
less limited. Perhaps many creatures would be "flat" to take full advantage of the
extended surface area.
Most of a 4-D creature's energy could be taken directly through a 4-D network of
pores, rather than ingested, because little space would exist inside for organs like a
brain and heart. The creature's nervous system might operate using electrical signals
oscillating through three dimensions and traveling through a fourth, creating a highly
complex synaptic web. The heart would have to work very hard if it were centrally
located and had to pump blood over great distances. Perhaps 4-D creatures would have
no central hearts but rather a mass of arteries to push blood along.