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To most people, the word computer conjures upan image of a PC sitting on a desktop. Accord-ing to a new study, however, complex compu-tations may also be underway in another bit ofoffice equipment: the potted plant that bright-

ens up the windowsill. Plants may perform what sci-entists call distributed emergent computation. Unliketraditional computation, in which a central processing unit carries out programs, distributed emergent computation lacksa central controller. Instead, large numbers of simple units inter-act with each other to achieve complex, large-scale computations.

Although the plants don’t add, subtract, multiply, or divide, theydo seem to compute solutions to prob-lems of how to coordinate the actionsof their cells effectively.

Many biological systems appear tocarry out this type of distributed com-putation—for instance, ant colonies,nervous systems, and immune systems.One favorite example among biologistsis slime molds, which exist for most oftheir lives as single-celled, amoebalikecreatures. When their food supply runsdry, they somehow figure out, throughlocal signals between cells, how to swarmtogether into a sluglike, multicellularorganism that produces the spores thatgive rise to the next generation.

Pinning down these computations inprecise ways has proved elusive.

The new work with plants is “the firstexperiment I know of where you canactually see what looks like a distributedcomputation taking place in a naturalsystem,” says Melanie Mitchell, who stud-ies distributed emergent computation atOregon Health and Science Universityin Beaverton. “That’s very exciting.”

A DELICATE BALANCE Plants mayuse computation to figure out how wide to open pores in their leaves,researchers propose in the January 27 Proceedings of the NationalAcademy of Sciences. The leaf pores, also called stomata, open toallow in carbon dioxide, which plants need for photosynthesis.However, open pores also let out water and so may dehydrate theplant. To balance these competing factors as environmental fac-tors change, plants constantly adjust how many and how widely theirpores are open.

The way that plants achieve this balance has been a mystery.There’s no brain to coordinate the tens of thousands of pores,

and individual pores seem to have no way of knowing what dis-tant pores are doing.

At first, biologists thought that each pore simply decided inde-pendently what action to take. About 10 years ago, however,researchers noticed that large patches of pores frequently openand close in concert. More recently, Keith Mott, a biologist at UtahState University in Logan, discovered that over minutes, thesepatches of synchronization move about the leaf, often displayingcomplex dynamics.

He described these observations to physicist David Peak, a col-league at Utah State. They reminded Peak of patterns that turn upin cellular automata, a kind of distributed emergent computer.

“It occurred to us that the patterns could be symptomatic of adistributed emergent computation,” Mott says.

SIMPLE AND COMPLEX Mott and Peak next investigatedwhether there was more to the seemingsimilarity between the behavior of leafpores and of cellular automata. A cel-lular automaton consists of a collectionof units called cells, each of which canbe in one of several states. Over time,the cells change their states accordingto rules that depend on their currentstates and those of their neighbors.

The best-known cellular automatonis the Game of Life, invented in 1970by British mathematician John Con-way, now at Princeton University. Thegame consists of a grid of cells, each ofwhich is considered to be either deador alive. At each time step, some cellsswitch state according to simple rules.For instance, a live cell with at leastfour living neighbors dies of overpop-ulation. Even though each cell is influ-enced only by nearby cells, complicatedglobal patterns can emerge.

In 2002, theoretical physicistStephen Wolfram argued in his book, ANew Kind of Science (Wolfram Media),that cellular automata may underlienearly all phenomena, from the physicsof elementary particles to life and intel-

ligence (SN: 8/16/03, p. 106). Most scientists don’t subscribe to such a sweeping vision, Mitchell

says, but cellular automata are being applied to a wide range ofquestions. They have been used, for instance, to process images andto model earthquakes, traffic patterns, and tumor growth.

In a cellular automaton with thousands of cells, it can be virtu-ally impossible to predict which kinds of global behaviors willemerge from which local rules. “It would be like trying to figureout what a computer is doing by looking at how voltages flicker upand down on the motherboard,” Peak says.

PATCHY INTERACTIONS — In the top image, aleaf’s pores (black passageways to the surface of theleaf) allow in carbon dioxide. Computations arisingfrom interactions between these pores may governthe formation of patches of open and closed pores.A chlorophyll fluorescence image (middle image)shows patches consisting of thousands of openpores (bright areas) or closed pores (dark areas).

COMPUTATION’S NEW LEAFPlants may be calculating creatures

BY ERICA KLARREICH

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In the mid-1990s, Mitchell—together with James Crutchfield ofthe Santa Fe Institute in New Mexico and Rajarshi Das of theThomas Watson Research Center in Yorktown Heights, N.Y.—tried a different approach to understanding cellular automata.Rather than design specific rules to produce a certain global behav-ior, the team used a genetic algorithm—which exploits the prin-ciples of Darwinian natural selection—to evolve cellular automatathat behave as the team had stipulated.

For instance, using cells that couldbe either black or white, the team pro-duced an automaton in which thecells flash in unison, alternatingbetween black and white. The teamstarted out with automata that eachhad random rules, then selected theautomata that came closest to thedesired behavior. They permitted thesurviving automata to exchange somerules with each other, mimicking sex-ual reproduction, and introducedsmall random mutations into theresulting rules. After many of thesegenerations, the resulting automatabehaved as the researchers had orig-inally specified.

This evolutionary success hints at how living creatures mighthave developed cellular automata, if indeed they have. Out of allthe possible interactions among living cells, evolution may haveselected interactions that give rise to useful computations.

LEAF DYNAMICSPeak, Mott, and their collaborators comparedthe movements of patches of synchronized pores in cocklebur leavesto those of patches of black and white cells in the automata thatMitchell’s team studied. Using fluorescence imaging, they trackedthe flux of open and closed pores on a leaf over 8-hour periods.

Patches of synchronization ranged in size from just tens of poresto tens of thousands of pores, and the patches moved about the leafover the course of minutes, the team found. The researchers alsomeasured what they call the “waiting time” between the appear-ance of successive patches in each pixel of the fluorescence images.The distribution of these waiting times, they found, obeyed a sim-ple mathematical law known as a power rule.

The scientists next compared the statistics of patch sizes andwaiting times to those of corresponding data in the cellularautomata. “The dynamics of the unfolding computation [in the cel-lular automata] looks statistically identical to what we see in thepatchiness of leaves,” Peak says.

The opening and closing of leaf pores is a subject that has been“studied to death,” says botanist Michael Frohlich, of the NaturalHistory Museum in London. “It’s amazing that something this sur-prising is found in a field that has been studied so hard for so long.”

Just which local rules might give rise to the global patterns ofopen and closed pores is a puzzle, Mott says. “The rules are the sin-gle hardest thing to deduce,” he says. Instead of trying to guess therules by working backward from the global behavior of the leaf, Peakand Mott are trying to create a computer model whose rules takeinto account the ways that leaf pores might influence their neigh-bors through hydraulic pressure and other mechanisms.

The real test, Peak says, will be whether their model producesthe same kinds of patch dynamics and carbon dioxide uptake thatbiologists have observed in leaves.

Cellular automata may give biologists a new framework forunderstanding how small-scale interactions can give rise to globalcharacteristics of an organism. “We have a wealth of informationabout cell-to-cell interactions, but the question is: ‘How do theseinteractions produce large-scale behavior?’ ” Mott says. “Perhapsdistributed emergent computation will provide us the tools tomake that jump.” ■

“It’s amazingthat somethingthis surprisingis found in afield that hasbeen studiedso hard for solong.”— MICHAEL FROHLICHNATURAL HISTORYMUSEUM IN LONDON

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