4 11
TOROIDAL PHENOMENA

lmplieu in our core model, and obvmus in Vlolent
delonarions sueh as aromie explosions, pulis irorn
diesel exliausl pipes. or deliberarely blawn as smoke
rings, are lhe rolling doughnul-shapes a! TORI. A
TORUS is a widespread nalural phenomenon The
dosed rnodels irigure dual enelose sueh a ionis, end
we ran imagine a slow-syrhng rorus or nulrienls
surrounding ihe siern ol any Km as errmndrip names
nuri-ienrs ro lhe ground, and lhe mis again rerurn
lhem Via rhesremol IM oee,

Phoiographir sulls ol alomie explosions may reveal
yiolenily roiarrng lori around and rrowning ihe
aseending eolunin or imuk: and deor . violenr
up—draughu caused by loeal hear rreale surh rori in
almospherie lherrnals, mueh appreeiaied by soaring
birds and glider pilols, who ride rhe inner iaseendingl
eurle oi lire doughnues oi hol air ihar ore generated, lor
example,uvrr deseris on hoiahemoens

A erunplex loroidal lorm is (he 'Robmson Com
gmnte“ irigure um, porrraying lhe sparetime lnrm
o: a mus—less parricle such as a pinion, represennng,
in died, annidared ion

DNA is also porrrayed as eneireling siren an
imagrnary pluHonis in riguie m A Mooius sinp-a
onesided rwisied loroid iolien porrrayed by MC
Eiduex in hII dM—enables us io eross an edge wrlhour
lining our penal Many hie iorrns produee rori leg
some sea snail egg masses) We reiy on a iorus ol
nipperl nllale our ryres and lo seal iamlar harrhes
as O—rings

A lorris is, in elieei, a speeial or lnineared ease or ihe
cueroeeli .el iriguie ml, as . loerus is a lruneaied
"iree‘. and (Zn or genera-ed by disrenlinuous or
explosive llow, or pulses in llow A lonis is a dosed
rhreedimensional yoriex One such elosed toroidal
lorrn, as lound in bhck holes, is shown in figun on
Here, aeereoon ol rriauer causes gaseous eyeerron ai the
poles, as she earlh may have 'elezled‘ seas and
eoniinenis al lhe magneiie poles, or gaihers in ihe
violeni energy ol ionised parricles that harm lhe
auroras, vislbk as polar ion in sarellne images, Even
lhe long eurrains n1 lhe auroras seen rrarn ihe ground
eonlarn yenieal spiral enluinnsll Reid pers Mum)

 

4.13

DIMENSIONS AND POTENTIALS;
GENERATORS

cur pmierned sysrems may exisr in lwo or more
dimensions, We ran reasellare twa—dimemlnlufly lair
need io enyisage rhiee dimeri * tor a me lorrn or
glaeier Ihe "924mm: ol rivers llow down along
S-shapud gradienlsr rlne generalor al' sueh a pauern is
grayiry 51nd dunes iorin on near-liar plauorrns or rhe
desen, and have wind as rheir generator, as do waves

88

 

on are sea Neilher gnwly nor wind may inneh aiieei
rne ereeping iree paiierns ol mosses, dendriles in
shales, or «he Inc-Illa iorrns ol rnyeorrhira in plan!
eells h is here rhar weseeour nee lorrn asrhe besi way
no grow or |0 galher nmnems in lhe dosenee oi yioleni
lsinelic pm The genera-or here is hle or gaowlh
irsell.

When kinehe [om do nor aei snongly, as in nu dud
essennally sheliered deserl environmenrs, lobulalion
and lanieing sull oeeur as ireezeihaw or swell-shrink
panerris, as they do in iee ilues on qulel ponds or in rhe
hexagonal pauerns ol siones on rundra, The slow
growlh ol crysiab inlo Mk eayihes or iee is snll relaied
io our general model: rhe generaior pl pauem here
being or ihe kvd oi moleeular iorees, as in many
purely eherniorl proeesses, and ihelorrris generrled are
iraelals

hi hill eounrry, energies are usually a eonilainanon oi
slream llow and grayily, On plains, ieepaeks or lial
snowlields, u I! fluzrlluw or lhe swelling ol rlay in
rain mat prodnees looularions or nerworks ol earih
pallems lohulauon, rlie produriion oi sueh shspes as

' re n, diners in origin and mode ol explvswn
lrorn rhe kineus-eneigy (flow) sysrerns we have been
discussing lsornehrnes lhmir oi lhe lohrilaied hours as

response oi name, or lile, lo s world lhsi lhreaiens
* odifimnm“.

ll lhe hills wear down, rhen lhe anrepenialhmaie
suriaees will produre (he)! lareral, rwodirnensional
lile pauerns, as does lhe lichen on a rock Kinerie
erosron pm: are lheri exehanged lur physieal and
ehermeal proeess ar the moleeular level, In“ even lhis
malts a sullieieni dilierenre in media in. lire iorrns io
expms themselves, and lor dillerenees ro arise in lhe
pairerris ol surlates,

 

  

414

CLOSED (SPHERICAL) MODELS,
ACCRETION AND EXPULSION

Allhough trees (includlng rree roorsl may lpproach
spherieal lorm, lhe hesl examples are lound in
spherieal bodies in spare. “meridian lighi, dusi, and
grs rowards hem, and may eapnue marshals, ln uyeir
early lormalion, lhey lhenuelyes may have had dense
eores rhal assembled rheir share ol galasrie normals,
and around ehese cores a lorus pl mauer ol low or
high-speed roialion ean lorrn. This is lhe model
presenied lor mosi oodles (Nm 5(nmll, 4 Apn| ‘35,
pp lzelol. A general model 7: green in Figure 4.11.

As mnku xeeurnulares in rhis way, bodies ean
respond py

. Becoming more dense- iii a lirrui oneu g/rmJF

. Swelling orexpanduig lprodueing shauer curds);
and

. gyeenng marenalai ine poles.

or any eombinarion ol lhese depending on lhe sure