Leaking down on a bare winier-declduuus bee, we see a lypiral iraelal, whrch we can also lind in lhe nilguriles isarid hised by lighrningl in sand dunes, and in lhe sharier zones ol explosions Tree roots are, in laei, a slow shaller nr explosion underground One way Io planl an apple iree in very hard gruund is lo delonale a small plug al gelignne a Yum or lwo belaw ihe surlace. lhe rooms will vallow ihe shaner palum, aml iunher elabomie ii. Seallers Mubptds may ar hisl seem lei presenl a class el events unrelaled lo eilher flow mudelr or Innshli, bui iracrals are being used l0 describe lhe scaners bl lree elumps in grassland, ar lichen on a sione in a sense, lhe surlace al spheroids crealed by branched phenomena (like lhe plan view 01 a lree rruwnl may shuw sueh apparenily randnm seallers as grawrh poinis, or a curved seeuoii shrough the cur or pnaned braiselus below lhe eiuwn ova nee wuuld also appear lo be a searier bl puinis (Figure mm These can be measured by iraeialanalysis. Fracial lheory may grve us a way lo measure, cumpuie, and design lor branched or seariered phenomena. bur we also need is undersiaird lhe physieal advanrages 9! developing ever rmrller canduils, Vngrl mall gives many insighrs inio ihis process and iis ellecis, Large sond are ol use ln mass lranspnri, bur barh the larninar llow paliems wiihin ihem and ihe laer lhai lhey havea small surlare area relalile m ihcir volume makes iheur inellicienl lor lhe ail/baron or maierials or lhe eondueiion o! heal aeruss iheir walls. Ever smaller rondulis have diileieni quail-res new is slow, alml lviseous in very small illbes or branches, direeliua changes in small branches are iherelure possible wilhoul ineurnirg iurlrulenee or energy losses Walls can be permeable, and ellleieni culleeiirrn, erehange, and lransler is eliecled (whdherci inalenals or physleal prsperlies such as heal and lighrl Many small epnduiis ellicienrly inlerpenelraie ihe exchange media Wherever ihere is a need (a calleel or dislribule maieeals, or Io irade boih ways wiih media, branching is an eneeliye response in design. lheieirrre, we need in use “mnny palhi“ in sueh siluahons as home gardens, where we are always lradlng nulricnu as our main aelivlly There is lime advaniage in lorrning ihese palhs as slraighl lines (spud is nor al lhe emense), but ralher in develop g a sel ul rill .1. ms or heyhuleshaped beds llhis is also lhe shape oi sacs in lungs) Cunyulured palhs rn gardens have lhe same eueei They eilher bring lhe gardener 1MB belier conrael wiih lhe garden, enabling colleelron and seryiring lo oecu r eieaie bener muiual exellange belweeir lhe spedes in lhe garden. The high-pressure/low-lluw naiure oi minor branches demands a very large luial eiosssecrional area bl ihese in relaliuir Io lhe main supply arreries. Such small eanduils may develop areas wruch m sum are 300-le limes ihal ul lhe supply arrery iour main nrads are lherellrre much less in area illan ihe laai vn lrachs rhar lead oii ihemi As an applied siralegy, muliiple small pallis enhanee aur aeeess lo loud sysielns, or in rm any syslem where we bmh lake and give maienals ln mgmlsms, lhe muluple braruhes give ihe being a chanee lo recover llvm iniury preserve inlurrnalion, and permir iegrowih in lhe evenl ol minor damage ii is a louleprboi sysiern oi inlerehange. Anoiher way to elled iniemhange is in elaboraie on lhe walls al larger enndulls by involuliuns, allached lins, irregular suriaees, or re ereaie spirals in fluids or gases by bending or s iralling lhe eenduils rhemselyes, and in general inducing a larger surlaer oi roniaei behveen ihe ulalerial branspoiled and the media wiih which we wish in udmlge nuirieiris, heal, or gases. branchrrig in lrees is as onen a mu“ oi errlernal larees lwind and sail pruning, secaceurs, or "used allaeki as il is a resull of mlernal cell panel-re; n is as much lomed upon Lhings as ii is lhe ~besl lhing he do: We musr lhereiure see lhe branched term as an inleraelian beiween an organism or process, lhe purpose ll serves, and ihe exlernal (Wm ul lhe media in which lhe organism is immersed (lhe lone: aeling on re exlmally io delorrn rhe perieel panernl Mung lhe slreainlines islesa el our model figuu Ln, iluids and gases may pass in eunduiis ar along 'lraumlsslon colds", [nod and srgnals are relayed lo eells, and gases exchanged. Organs served by or serving ihese syslems are hallsmodels 0! our iree lhidireys, lungs» or branching lradals lmesenrerresl No mailer how long or rompkx conduiis are, in die end lhelr eonienis diverge, eseape, and disperse, and ac llie iniahe malerials are galllered Emm dlspersed saurees li is ilus galhe g and dispersal hum bolh FIGURE 4.2: NW1“!!! raerialised lur dilluslbn ul inlusibn llunirs, llmn-yx, muthms. palm has) ii usualysvhlrnla blallmlnvr and was»: a hall-mane in an. madluin lhe alvihli oi lhe lunux hinhei tar-ml: ihe mm: an: en a mud-elem semen