Physarum polycephalum

1cm

Physarum polycephalum

Solving maze

Discrete Form

2N

jN

iN

1N

ijM

Discrete Form

1ijM

iN jN

2ijM

Discrete Form

2N

jN

iN

1N

ijM

Start point

Goal

1N

2N

iN )(tip Pressure

ijM ijL

)(tijD

)(tijQ Flux

Length

Conductivity

Modeling of the flux of the sol

)( jiij

ijij pp

L

DQ

iN )(tip Pressure

ijM ijL

)(tijD

)(tijQ Flux

Length

Conductivity

)(tip Electric Pressure

)( tij

ij

D

LElectric Resistance

)(tijQ Electric Current

Kirchhoff law

jN

2,1j0 iij Q

1N

0I

FS2N

0IFS

Electric sources

0

0

0 2

0 1

I Q

I Q

ii

ii

Modeling of the tube growth

ijij rDijQD

dt

d || r :degenerate rate

(constant)

time

rijQ ||

ijD )(tijD

Model equations

Flux of sol Tube growth

ijij rDijQD

dt

d ||

2,1j

0

0

0 2

0 1

I Q

I Q

ii

ii

0 iij Q)( ji

ij

ijij pp

L

DQ

T shape vessel

The tube at dead end disappears

Ring shape vessel

Only shortest tube remains

)( 212

112 LL

Stable equilibrium pointUnstable equilibrium point

Ring shape vessel

Both tubes remain

)( 212

112 LL

Stable equilibrium pointUnstable equilibrium point

Solving Maze

Solving Maze

スタート

ゴール

Solving Maze

スタート

ゴール

Apply for road navigation system

START

GOAL

1. We can reproduce the adaptive network of the true slime mold.

2. “Physarum Solver” can find the shortest path.

Summary

1. Simulation with many food sources

Current Work

That’s all. Thank you very much!!

Apply for road navigation system

START

GOAL

Ex 2. Shortest path on Weighted graph

food

food

Ex 2. Shortest path on Weighted graph

nyflexibilit

region

：：

nyflexibilit

region

：：

Ex 2. Shortest path on Weighted graph

ijij DrijQD

dt

d)(|| x

1

3)(xr

Solving Maze

START

GOAL

Does physarum have enough intelligence to solve the maze?

Shortest Path From Seattle to Houston

Ex. 3 Path choice

food

vessel

Physarum

Model Equation

ijijij rDQDdt

d

Model of Tube Growth

One(Short)

Both

180180

1

1

10

)1(

Both tubes remain

Stable equilibrium pointUnstable equilibrium point

Simulation Result

)1(

Almost all tube remain

数値シミュレーション

)1( Simulation Result

One tube remains (chose by initial condition )

Simulation Result )1(

Stable equilibrium pointUnstable equilibrium point

One tube remains (chose by initial condition )

数値シミュレーション )1(

Simulation Result

One(initial condition)

One(Short)

Both

Both

180180

1

1

10

ijijij rDQDdt

d

Model of Tube Growth

Model Equation

Q

jiD

1

1

ijij rDQ

QD

dt

d

1||

||

01||

||

ijrDQ

Q

)3(

Simulation Result with each 0I

Flux

Number of the tube

Both tubes remain

)0.3(1||

||0

IrDQ

QD

dt

dij

ij

ijij

Simulation Result

Application

Application

Thank you for your attention!!

a2 Q

Modeling of the flux of the sol

FluxPoiseuille Flow

ij

jiijij L

ppaQ

)(

8

4

8

4ij

ij

aD )( ji

ij

ijij pp

L

DQ

Ex 2. Shortest path on Weighted graph

ijjiij

ij LrppL

D)(x

partlower

partupperr

3/11

3/23)(x

ijji

ij

ij LppL

Dr ˆˆ)(

x

ijijij DrQDdt

d)(x

)0.2(1||

||0

IrDQ

QD

dt

dij

ij

ijij

One tube remains

Simulation Result