riveis, rrees, eloiads, animals, and landlonns generally
as a sel oi shapes, appaierirly uuielahed lo each olher,
al least as iar as a eemmon underlying pauei-n is
soueemed Whal do we see’ We ean liil some ol in.
visilile looms as follnws:

- wovss ori waler aud "hoe as ripples in dunes
and saudslones, or iassilised quaruiles and slaees.

« srlzzixMLlNEs, as loam siripa on wales, and in
siieams rheinselves

. CLOUD lows in iravernne (puma: ealeire fmm
hol springs», iree owns, and “Fully" rlouds or as
rloiid slieains,

- SPIRALS in galames, sunilowers, rhe glohal
eneulahou ol air, whmpmli, and ehams of islands in
an:

. LosEs, as ar lhe edge ol reela, in liehens, and
lrmgmg diehordeis Msall pans

- BRANCHES, in new and soeauis eonveigiug or
dlvelgmyexw esharrer mes

. scnmzs ol algae. lree clumps in swamps,
islands, and liehens on moles

- NEIS as eraeles in mud, honeyeornh, iuside bird
bones, in iheeolui-unsol oasalrlas viewed lioiri shovel,
and (lens ol rising and lallmg air on desens

 

 

The was or marks in mud and eoolmg lava are
shrinkage panems raused nm by llow or growih. our
oy rhe Yawn! revision ol drying or eooling, as are many
parrerns in ieellows and lhe eraelsed pauern ul poilerv.
or lhe eraeks in bar): on liees. Thermal wind eells arise
al rhe sonlluenee ol large heal cells on deserl lloors.
ioriniug a nel paliern il viewed lioiri above or oelow

in all ol lhese eulegories, I hope lo show ihar one
iriasier pairern o applieaole, and lhal eiieu lhe bodies
oi animals are made up ol bones, organs. and muscles
ol one or inoie ol lhe lax-ms above 1 will link these
phenomena—generaled by growlh and "W7 lnro a
single model loi-in. Thai [mm is a slylised liee iriguie
m Around um eeniral rree lorm ol rhis model are
arranged various eiosseseeiions. plans, longiludinal
seerions, and srieamliue palhs, all derived lroin real

seelioris, palhs, or pioieelioris ol rhe me.

The evoluiiou ol sueh a lorm lioin an inihal pomi in
spacedlmr, l call an EVENT sueh evenls can lse
ahsimol or palpable. They have m soi-ui-nou an origin
lol, a phase ol giowrh ln-‘le- an expression ol iheir
energy polenlioll. dzcay, and dissoluriou inio olher
evonrs ol a likz or unhke lririn. The eveur ol a nee is al
leasi |hvu~dimensmnzL and musr be lhoughl oi as
exreudiug mo and oul or a plane 1F). However, many
similar evenis inch as migralion panei-ris or glacianou
ean he as well porirayed (As lhey are seen in aerial
phorographsl as rwodimensional

nie curvilinear S1REAMLINES 1959), are seen lo
eurve or spiral ihiough rhe Origui, rust as iin lam lhe
phloem lsroiage eellsl and xylsrn lsaphearing eellsl
spiral rhrougli lhe xex‘ axis, or earrh suriare plane m,
ol a ieal iree, Not so easy Io ponray is lho laer lhal rhe
xylem is rxltnull io llie slems and unusual lo rhe rools,
and lhe phloem rhe seveise Al a zone in rhe plane ml,

72

lhereloie, lhese oells INTERWEAVE or eroas over as
rhey spiroloui oloriulo rhe med'

This deeeprively simple ~apple soie' or rree shape.
sp lling oulol lhe plane il- isasloweinoving yoneir
such as we see in lorriadoes and whirlpools Tnlflc
lhiougri lhe slieai-uliues is in bath dlnzlwns, in m,
iugais and pholosyulheoo pmduus rravel iron. aown
ro iool margin, and waler and minerals lioin rools ro
erown. Thin, each margin oi our panern is born
eolleelmg and disrrihuling malerials lroin diilerenr
media. The rree lrades horh ways wilh eleoieurs or lhe
media, and lhere is an aeiive waler and gaseous
exenauge wlth (he media (M1. M2) Two—way irude is
she normaliry oi plauls, organs, Im‘l uaiuial lormo

As we know, a erosseiiiola eree slem, lhe hasisoirhe
srudy ol dendioehronology, reveals a largel panern ol
expanding growih loy which rhe reee adds bulk
anuuallyl and hom whlch we ean diseoyer much aoour
pasi oeeurreuses ol droughl, seaaoual ehariges,
aunosphei-ieeomposiron, rise, and wind iriguie u—lrl

Sanw palms lpandanvs spp l ol lhe liopirs develop
ascending ikzm spiials. very remmiaseor ol lan iuroiue
blades, and sunllowers eieale open seed spirals lin lwo
diiesiioual, so eoniinon in many whorled plaurs, rhe
slem iisell lorees open an ever-expanding llow
rhiough rhe xev plane herweeu lhe media, allowing
more malerial lo pass rhrnugh as rime aeeumulales
rhe eveni expands ihe in al ruplure ol ihe suiiaee
herween lhe media, allow g giearer now io uh plase,
and lliis we is ieeorded in lhe largel paliern ol rhe
seem, ar lhe poxm or gennrnarion mm mm lei.

 

 

4.3
MATRICES AND THE STRATEGIES
OF COMPACTING AND
COMPLEXINC COMPONENTS

A sei oi inlerseelrng sine waves developed over a
regular square or hexagonal malrix will sel up a
surlaee eoiriposed ol our one model shapes, ll doesn-li
i-uarrer ilwe see lhe sine waves as sraoe or nowiug, lhe
eoie model will sail mainrain irs shape, and llow in rhe
sysrom does nor necessarily delorin lhe pauern. Sueh a
pallern malrix lrlgure 4.2: shows rhal our models
leirellaie lliom rhe laiin iesserie, meaning iilesl io
ereale whole suriaees ll landsnpc are, in laer, a see ol
sueh models, they musl he aole ro lessellale

Convee n eells on desens arise lrorn a roughly
hexagonal malrix ol air eells 1—5 kin aeross, and
riiazriees also underlie ihe spacing oi nees loiesls

olaeial laudseapes show whole series 0! sueh
pallerns, as do regular river headwaiers We eould
equally well have erealed a marrix by adding in
samples ol our core pallem as we add riles m a floor,
Thus we see (he Euelideari eoneepl ol poiues and lines
underhes our eumliuear lorms. Even ii-iegulai models
inguie Lil lessellale Sueh resssllae are sen-red on
neis or iegular grids