beyond lhe rigour ol lhe srrriple Euelidean regu- larilies beloved ol leshnologisls and arehileels, lhm remains mosl (m alll ol narure Naluie imperleelly round, never llal or square, linear only liar mlanrlesunal disrariees, and slubbomly abnormal. Nalure llowing mwling, (lying weeping, and in apparenl duaniy. Nalure beyond pnclse measuremenl, and romprehenslble only as serisalion and syslem Nalhlngwemnolaserve is regular, p-my because we ourselves are unperleel observers We lell lorruiies lor w llieml on llie wrirhing ol enrrails or ralnode ray graphias, on lhe xiflm ol dise or bans, or an ai-iays ol mum. Are lhe readings ol lea leaves any less reliable lhan lhe pruieelions ol pollslersl Regular rhings are rhose lew lhal are meehaniral iir shaped lleiriporarilyl by our own rem-med wmld view, llaey soon bemnie irregular as rime erodes lllei-ri Trulh, lrlie lhe worldrlianges in response lomlormanon There are ar leasl lhese wonhwliile rashs lo allempr l. A MollE GENERAL PATTERN UNDERs STANDING, bolli as anemprs al loi-rmrig more gmwnl pallern models, and as exnmpks ol rialural phenomena lrial demanslrale such models 2 A UNKING DISCXPUNE lhal equally apples lo geography, geology, rriusie, irl, asrronomy, parliele physics, eeonamus, physiology, and reelinology Thls linhing discipirie wnuld a ly lo eonse us design irsell and m lhe inlormalian lluw and rransler praeesses |hil underlie all our diseiplrnes. Such a unilying roneepl has greal relevanre lo eduealirm, al every level lioin primary lo posl—graduale disciplines 3 GUIDES lo PATFERN APPLICATION, some ex- arriples of how applied palleming Ichuves our desired ends iii everyday lile, where role learnrng, lirlear llurlllirig or Eudldull geoialelry have all lailed lo aid ur in lorinularlng suslamable selllenlenls lr is iii lhe appliealiorl el harmonie pallems lhal we derrionslrale uurcomprellension ol lhe mearurig ol naruie and hle mere have been many books all me subieel ol sym- bols, palrerris, growlh, lurni, delormalion, and symmelry The aulhors ullen abandon llle (XHEIW shorl ol devising general models, or rusl as a salis» l-Iclory mirhemarieal soluliun is evolved lor one or more pallei-ils, and almosl always beloae allempririg la eieale applied illuslralionsol how rheirellons assisl us in practical lire allairs, Some are merely eoribenl lo lisl mmplesi or lo mahe eaialogues ol phenomenaoahers prelend lhal meanings lie in pallern or number alone—dial panems are symbols ol arcane knowledge. and lhey asserl lhal only an unqueslloned belrel unloeld lhair powers The simple pailern models ligured herein are in- lended id be a uselul adluriel lo designers and eduealois They also illuslrale how we can pomay our lrurilririg aboul lire, landscapes, and lhe rorrirriunaliry lhal rs niluie learning a niasler pallem is very like learning a pi-ineiple. ir may be apphcabk over a wide range at phenomena, some eompler and some simple As an abslraelioii, ll assisls us lo gain meaning lilim llle and laridseape and lo comprehend allied p’wflomtna. One ean spend endless hours seeking lurlher reirnlilir, mysrieal, or bopologieal insighls mlo pallem. 'nle proeess is addieliye, and I am as unwilling lo abandon llilseliaprer as lwas lo slarl ll, bull Ims| iliaa olhers, beller equipped, Will expand and lurlher exphin rlie basie eoneepls i believe rhal ii is in sophisliealed palrern appllcallon lhal lhe lulure or design lies, and where many solulions lo innaelable problems may be lound We have a good grasp on lhe behaviours ol pallerri iri iialural phenomena il we can explain lhe smmm mings lin lernis ol lheir general pailerli olilhnrsl; llie nelworlrs and BRANCH|NG ol lriburaries lgalhering llowsl and dislribularies ldispersal ilowsl, llle mums and flow regulanori wllhm olganlsms or |M elerrieiils oi wind, waler, and magma, and illuniinale how SCATTERED PHENOMENA aiase rurllier, ll WAVE phenomena and sulEllMust are rurilained wilhin our pallern analysrs, as real waves or as liirie pulses, rhese and lheir reliaelioo and rnrerlerence pallerris lurm anolher sel or pallern generalors, responsible lm roasls, elouds, winds, and lurbuleril or sl-reamlined liuw And, il we can sliow how lhe pallerri ourhnes ol landscapes, slelelal pails, or New phenomena lil logelher as MATRICES (lmulodung selsl. or arise lrorn sueh malrlees leg. whrrlwinds lmm lheianal eellsl, lheri we ean generale whole landkape syslrnis or eomplele organisms lrom a mosdk al sueh pallerns ln nirure, eyenls an ordered or spared in dlscme unrls There are smaller and larger orders ol evenls, and ilwe arrange like loriris iii lheirardrrs, we Will lind chislees ril measures ar cerlain sires, volumes, lengllas, or other drrnerisioris. This is lrue lor river branehes, sooal easles. aelrlerrlenl sire. marsupials ol lhe same loriri and arrays ol dunes, planels, or galaxies, in llle folluwlng pages, l W)“ lry lo irirlude all lhis and lo derive il lroiri lhe basis ol a single simple model lrigure ml, which, underslood in all ils pans, has eaeh ol lhese phenomena, and a gieal many more sublle inleienles, williiri il Nor all, or even rriany, ol lnese shapes, symbols, syrrimelries, sealleis, or lorms will be mdivlduflly descnbed or hguied here. bul lhe bask parlerrl pails be lanelly described and relaled lo eaeh olher The basir model ilsell is derived harm a 'scd rree lorin We should nol ronluse lhe comprehension oi mm wuh lhe knowledge 0! SUMANCEi llle map is rim Lhe lemmry‘ibnl an underslariding ol iorrn glves us a beller comprehension ol luneliori. and suggesls appropnale slralegies lor design 41 A GENERAL PATTERN MODEL OF EVENTS When we look abuur us in me world, we see me hills, 71