The Games and Puzzles Journal, #8+9 - Mayhematics

page 148 THE GAMES AND PUZZLES JOURNAL issue 8+9
MATHEMATICAL A"RT
The first two patterns here are given to show that the pattern resulting from the application
of a growth-rule, proceeding step by step in stages, is not necessarily of the unpredictable
ortfractal-kindr.such as were illustrated in earlier issues, but can be perfectly regular.
SQUARE FLOWER
Starting from a central square' the
sides are extendedr curving to meet
at f our new points that are the corners
of a larger square resulting in a type
of octuple spiral a pattern grown
by a process of tcontinuous extensiont.
LATTICE OF CIRCLES
Starting f rom a central unit circle,
at each stage circles are drawn centred
at the nearest unused lattice points,
to touch the existing pattern. The result
is a very si m ple regular pattern, not
at all complex or torganiet.
CROSS-EYED OWL
From a central spot a single ttwigt grows
upwards. Thereafter f rom any free
twig end two new twigs grow at right
angles until they are of unit length
or meet another part of the growth.
Growth ends when the initial point
is reached once again.
STREWBERRY FIELDS
Seeds are planted at regular intervals
(of 4 + 3l\/2 units) apart. Each grows
f our shoots at right angles, then each
of these branch out in pairs of shoots
at right angles. Shoots only grow if
they have room to reach f ull (unit)
length, without m eeting an existing
part of the growth.