Algorithms in Nature

Slime mold network design

Physarum polycephalum

1cm

Physarum polycephalum

Discrete Form

2N

jN

iN

1N

ijM

Start point

Goal 1N2N

iN )(tip Pressure

ijM ijL

)(tijD

)(tijQ Flux

Length

Conductivity

Modeling of the flux

)( jiij

ijij pp

LD

Q −=

iN )(tip Pressure

ijM ijL

)(tijD

)(tijQ Flux

Length

Conductivity

)(tip Electric Pressure

)( tij

ij

DL

Electric Resistance

)(tijQ Electric Current

Modeling of the tube growth

ijij rDijQDdtd

−= || r :degenerate rate

(constant)

time

rijQ ||

ijD)(tijD

T shape vessel

The tube at dead end disappears

Ring shape vessel

Only shortest tube remains

)( 212

112 LL ≠

Stable equilibrium point Unstable equilibrium point

Ring shape vessel

Both tubes remain

)( 212

112 LL =

Stable equilibrium point Unstable equilibrium point

Solving Maze

Apply for road navigation system

START

GOAL

Using constraints for limiting search space

food

food

Ex 2. Shortest path on Weighted graph

ijij DrijQDdtd

)(|| x−=

=13

)(xr

Slime Mold: Rules for Biologically Inspired

Adaptive Network Design

Tero et al. Science 2010

Network design

• At each iteration select two random points • One acts as a food source, the other as the sink • Compute flux between them based on all other points / tubes in the graph

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

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

Summary

1. What about multiple food sources?