Towards Logic Circuits based on Physarum Polycephalum Machines

The Ladder Diagram Approach

Andrew Schumann

, Krzysztof Pancerz

1,2

and Jeff Jones

University of Information Technology and Management in Rzesz

ow, Rzesz

ow, Poland

University of Management and Administration in Zamo

c, Zamo

c, Poland

University of the West of England, Bristol, U.K.

Keywords:

Physarum Polycephalum, Logic Gates, Ladder Diagrams, Unconventional Computing, Nature-inspired

Computing.

Abstract:

In the paper, we present foundations of logic circuits based on Physarum polycephalum machines. We propose

to apply the ladder diagram approach for constructing topological structures of such circuits. Relationships

between basic ladder diagram elements and topological constructions present in Physarum polycephalum ma-

chines are emphasized. At the beginning, basic logic gates (AND, OR, NOT) are considered. Such a set of

gates constitutes a functionally complete system. This fact is important for building computationally universal

devices.

1 INTRODUCTION

Physarum polycephalum is a one-cell organism be-

longing to the species of order Physarales, subclass

Myxogastromycetidae, class Myxomycetes, and divi-

sion Myxostelida. In the phase of plasmodium, it

looks like an amorphous giant amoeba with networks

of protoplasmic tubes. It feeds on bacteria, spores

and other microbial creatures (substances with a po-

tentially high nutritional value) by propagating to-

wards sources of food particles and occupying these

sources. A network of protoplasmic tubes connects

the masses of protoplasm. As a result, the plasmod-

ium develops a planar graph, where the food sources

or pheromones are considered as nodes and protoplas-

mic tubes as edges. The plasmodium may be used for

developing a biological architecture of different ab-

stract devices, among others, digital. Plasmodium’s

ability to perform useful computational tasks, in its

propagating and foraging behavior, was ﬁrstly em-

phasized by T. Nakagaki et al. (cf. (Nakagaki et al.,

2000)). In Physarum Chip Project: Growing Com-

puters From Slime Mould (Adamatzky et al., 2012)

supported by FP7, we are going to implement pro-

grammable amorphous biological computers in plas-

modium of Physarum. This abstract computer we are

going to obtain is called slime mould based computer.

One of the tracks in the project is to develop a new

object-oriented programming language for Physarum

polycephalum computing (Schumann and Pancerz,

2013).

The problem of constructing logic gates in chem-

ical media or on biological substrates has been con-

sidered earlier in the literature. Different approaches

have been proposed. One of them is to constrain

the substrate into channels and allow disturbances to

propagate along the channels and interact with other

disturbances at the junctions between the channels.

For example, this approach has been implemented

in a geometrically constrained Belousov-Zhabotinsky

medium, cf. (G

orecki et al., 2009), (Motoike and

Yoshikawa, 2003), (Sielewiesiuk and G

orecki, 2001),

(Steinbock et al., 1996). Also, non-excitable chemi-

cal implementation of logic gates has been proposed

(Adamatzky and De Lacy Costello, 2002). A wider

discussion of Physarum polycephalum gates is in-

cluded in (Adamatzky, 2010).

Our approach, presented in this paper, is a lit-

tle different. We propose to construct logic gates

through the proper geometrical distribution of stim-

uli for Physarum polycephalum. This distribution is

determined according to ladder diagrams (Rosandich,

1999) representing basic logic gates (AND, OR,

NOT). Rungs of the ladder can consist of serial or

parallel connected paths of Physarum propagation. A

kind of connection depends on the arrangement of re-

gions of inﬂuences of individual stimuli. If both stim-

uli inﬂuence Physarum, we obtain alternative paths

165

Schumann A., Pancerz K. and Jones J..

Towards Logic Circuits based on Physarum Polycephalum Machines - The Ladder Diagram Approach.

DOI: 10.5220/0004839301650170

In Proceedings of the International Conference on Biomedical Electronics and Devices (BIODEVICES-2014), pages 165-170

ISBN: 978-989-758-013-0

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

for its propagation. It corresponds to a parallel con-

nection (i.e., the OR gate). If the stimuli inﬂuence

Physarum sequentially, at the beginning only the ﬁrst

one, then the second one, we obtain a serial connec-

tion (i.e., the AND gate). The NOT gate is imitated

by the repellent avoiding Physarum propagation.

The rest of the paper is organized as follows.

In Section 2, we recall basics of Physarum poly-

cephalum machines with a special focus on stimuli.

Section 3 mentions a basic idea of ladder diagrams.

This idea is used in Section 4 for constructing logic

gates based on Physarum propagation. Section 6 sum-

marizes the presented approach and suggests direc-

tions for further work.

2 BASICS OF PHYSARUM

POLYCEPHALUM MACHINES

In Physarum polycephalum machines, we can dis-

tinguish the following stimuli constituting their data

nodes:

• Attractants that are sources of nutrients or

pheromones, on which the plasmodium feeds.

Each attractant A is characterized by its position

and intensity.

• Repellents. Plasmodium of Physarum avoids

light and some thermo- and salt-based conditions.

Thus, domains of high illumination (or high grade

of salt) are repellents such that each repellent R is

characterized by its position and intensity, or force

of repelling.

Plasmodium of Physarum polycephalum functions as

a parallel amorphous computer with parallel inputs

and parallel outputs. Data are represented by spa-

tial (topological) conﬁgurations of attractants and re-

pellents. Plasmodium of Physarum polycephalum

is a computing substrate. In (Adamatzky, 2010),

Adamatzky underlined that Physarum does not com-

pute. It obeys physical, chemical and biological laws.

Its behavior can be translated to the language of com-

putations. At the beginning of computation, data

nodes are distributed in a computational space, and

plasmodium is placed at given points in the space.

Plasmodium proceeds computation even if the solu-

tion has been reached and halts only when physical re-

sources are exhausted. Typically, plasmodium spans

attractants (sources of nutrients or pheromones) with

protoplasmic tubes (veins). Plasmodium builds a pla-

nar graph, where nodes are attractants and edges are

protoplasmic tubes.

It is a subject of discussion how plasmodium feels

attractants. Experiments show that plasmodium can

locate and colonize the nearby sources of nutrients

or pheromones (attractants). In our approach, we as-

sume that each attractant (repellent) is characterized

by its region of inﬂuence (ROI) in the form of a circle

surrounding the location point of the attractant (repel-

lent), i.e., its center point. The intensity determining

the force of attracting (repelling) decreases as the dis-

tance from it increases. A radius of the circle can be

set assuming some threshold value of the force.

3 BASICS OF LADDER

DIAGRAMS

Ladder logic is the most popular programming lan-

guage used to program Programmable Logic Con-

trollers (PLCs), cf. (Rosandich, 1999). This lan-

guage was developed from the electromechanical re-

lay system-wiring diagrams. Programs in the ladder

logic language are written graphically in the form of

the so-called ladder diagrams. Basically, this nota-

tion assumes that contacts are controlled by discrete

(binary) inputs and coils control discrete (binary) out-

puts. We can distinguish three main types of elements

of ladder diagrams:

• Normally open contact (NOC). It passes power

(i.e., it is on) if the binary input assigned to it has

value 1. Otherwise, it does not pass power (i.e., it

is off ).

• Normally closed contact (NCC). It passes power

(on) if the binary input assigned to it has value 0.

Otherwise, it does not pass power (off ).

• Coil (C). If it is passing power (i.e., it is on), a

value of the binary output assigned to it is set to

1. Otherwise (i.e., it is off ), a value of the binary

output assigned to it is set to 0.

The symbols of ladder diagram elements mentioned

earlier are collected in Table 1.

Table 1: Symbols of main types of elements in ladder dia-

grams.

Symbol Meaning

Normally open contact

Normally closed contact

Coil

Using three main types of elements of ladder dia-

grams we can build basic logic gates shown in Figures

1 (AND), 2 (OR), and 3 (NOT).

The gates mentioned work as follows:

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Figure 1: The ladder diagram AND gate.

Figure 2: The ladder diagram OR gate.

Figure 3: The ladder diagram NOT gate.

• AND: The coil is on (Y = 1) if and only if both

contacts are on. It is satisﬁed if A = 1 and B = 1.

Otherwise, the coil is off.

• OR: The coil is on (Y = 1) if at least one contact

is on. It is satisﬁed if A = 1 or B = 1. Otherwise,

the coil is off.

• NOT: The coil is on (Y = 1) if a contact is on.

A = 0 causes the contact to be switched on. The

coil is off (Y = 0) if a contact is off. A = 1 causes

the contact to be switched off.

Using structers of basic logic gates we can build,

in ladder diagrams, more complex digital systems.

Now, it is out of scope of this paper. We will con-

sider this problem in the future.

4 LOGIC CIRCUITS BASED ON

PHYSARUM POLYCEPHALUM

PROPAGATION

Ladder diagrams implement an idea of ﬂowing power

from left to right. The output for the rung in the lad-

der diagram occurs on the extreme right side of the

rung and power is assumed to ﬂow from left to right

if and only if there exists at least one closed path from

left to right making the ﬂow possible. We apply this

idea to build logic gates in Physarum polycephalum

machines. Flowing power is replaced with propaga-

tion of plasmodium of Physarum polycephalum. Plas-

modium propagation is stimulated by attractants and

repellents (see Section 2). In our approach, stimuli

(attractants and repellents) are treated as data nodes.

We assume that plasmodium must occur in a proper

region to be inﬂuenced by a given stimulus. This re-

gion is determined by the radius depending on the in-

tensity of the stimulus. Using the analogy to ﬂow-

ing power in rungs of ladder diagrams, we can build

logic gates in Physarum polycephalum machines by

the proper geometrical distribution of stimuli (attrac-

tants and repellents) on the substrate. Controlling the

power ﬂow in rungs by opening/closing contacts is

replaced with controlling the plasmodium propaga-

tion by activating/deactivating stimuli. Relationships

between elements of ladder diagrams and stimuli of

Physarum polycephalum computing are collected in

Table 2.

Table 2: Relationships between elements of ladder dia-

grams and stimuli of Physarum polycephalum computing.

Ladder diagram element Physarum polycephalum

computing stimulus

Normally open contact Attractant controlled by input

Normally closed contact Repellent controlled by input

Coil Attractant controlling output

Table 3 shows interpretation of logic values (0 and

1) for inputs in terms of states of stimuli. Input val-

ues cause activation/deactivation of stimuli. Value 1

activates the stimuli whereas value 0 deactivates the

stimuli. Analogously, Table 4 shows interpretation of

logic values (0 and 1) for outputs in terms of states

of stimuli. In our approach, the output represented by

the coil in ladder diagrams is replaced with the attrac-

tant. We assume that the output attractant is always

activated. If plasmodium is attracted by it and occu-

pies it, then we interpret this state as 1. Otherwise, if

there is no plasmodium occupying the attractant, i.e.,

plasmodium is not attracted, the state is interpreted as

Table 3: Representation of input logic values.

Boolean value Representation

0 Attractant/repellent deactivated

1 Attractant/repellent activated

Table 4: Representation of output logic values

Boolean value Representation

0 Absence of Physarum at the attractant

1 Presence of Physarum at the attractant

Our idea of paths of plasmodium propagation is

further presented graphically. In Table 5, we have col-

lected symbols used by us in diagrams.

As it was mentioned earlier, the idea of ladder dia-

grams has been applied in our logic gates constructed

in Physarum polycephalum machines. Figure 4 shows

distribution of stimuli for the AND gate. This distri-

bution simulates a serial connection of contacts. Plas-

TowardsLogicCircuitsbasedonPhysarumPolycephalumMachines-TheLadderDiagramApproach

167

Table 5: Symbols of elements used in ﬁgures.

Symbol Meaning

Physarum

Attractant deactivated

Attractant activated

Repellent deactivated

Repellent activated

Region of inﬂuence

Direction of plasmodium propagation

modium of Physarum polycephalum P can be prop-

agated to the output attractant A

if and only if both

attractants A

and A

are activated. First, plasmod-

ium is attracted to A

(because it is placed only in

its region of inﬂuence). After the achievement of this

goal, it is in the region of inﬂuence of A

and it is

attracted by it. The achievement of A

causes that

plasmodium is in the region of inﬂuence of A

and it

is attracted by it. Finally, plasmodium achieves A

. It

is interpreted as a logic output with value 1. Deacti-

vation of either the attractant A

or A

causes that

the path of propagation becomes broken, i.e., there

is a place where plasmodium is not attracted by any

attractant. Figure 7 shows paths of plasmodium prop-

agation for all possible combinations of input values

for A

and A

Figure 4: The Physarum AND gate.

Figure 5 shows distribution of stimuli for the OR

gate. This distribution simulates a parallel connection

of contacts. Plasmodium of Physarum polycephalum

P can be propagated to the output attractant A

one of the attractants A

or A

is activated. First,

plasmodium is attracted to A

or A

(because it is

placed in regions of inﬂuences). After the achieve-

ment of one or both of them, it is in the region of

inﬂuence of A

and it is attracted by it. Finally, plas-

modium achieves A

. It is interpreted as a logic output

with value 1. Deactivation of both attractants A

and

causes that the path of propagation becomes bro-

ken, i.e., plasmodium is not attracted by any attrac-

tant and cannot start from the initial position. Figure

8 shows paths of plasmodium propagation for all pos-

Figure 5: The Physarum OR gate.

sible combinations of input values for A

and A

The NOT gate behavior is simulated by the repel-

lent as it is shown in Figure 6. If the repellent R

activated (i.e., the input value is 1), then it avoids plas-

modium to be attracted by the output attractant A

Therefore, Physarum is not present at A

, i.e., the out-

put value is 0. Otherwise, plasmodium is not avoided

and achieves A

. Figure 9 shows paths of plasmod-

ium propagation for all possible combinations of in-

put values for R

Figure 6: The Physarum NOT gate.

a) b)

c) d)

Figure 7: States of the AND gate for all input combinations.

5 EXPERIMENT

In the experiment, we have built a Physarum poly-

cephalum demultiplexer based on the ladder diagram

structure. A demultiplexer is a device taking a single

input signal and selecting one of many data-output-

lines, which is connected to the single input. In Figure

10, a schematic symbol of the 1-to-2 demultiplexer

(a) and its implementation (b) using a particle model

of Physarum polycephalum (Jones and Adamatzky,

2010) are shown. In the schematic symbol: d is a

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a) b)

c) d)

Figure 8: States of the OR gate for all input combinations.

a) b)

Figure 9: States of the NOT gate for all input combinations.

data input, s is a select input, and y

, y

are outputs.

The operation of the demultiplexer can be described

as follows:

• if s = 0, then y

= d,

• if s = 1, then y

= d.

The functional speciﬁcation can be written as y

sd and y

= sd. In the Physarum polycephalum

implementation of the demultiplexer, one can see:

Physarum polycephalum (P), attractants (A

, A

), repellent (R

). Let ROI denote the region of in-

ﬂuence. For the topological distribution of Physarum

polycephalum, attractants and repellents, we assume

that:

• P belongs to ROI(A

• A

belongs to ROI(A

), ROI(R

), and ROI(A

• A

belongs to ROI(A

Logical states are implemented in the following way:

• s = 0 means R

and A

are deactivated, s = 1

means R

and A

are activated,

• d = 0 means A

is deactivated, d = 1 means A

activated.

It is worth noting that A

and A

are always acti-

vated.

a) b)

Figure 10: 1-to-2 demultiplexer: (a) a schematic symbol,

(b) distribution of stimuli.

In Figure 11, the experimental environment for a

particle model of Physarum polycephalum is shown.

Figure 11: The experimental environment for a particle

model of Physarum polycephalum.

In Figure 12, results of experiments are pre-

sented. Pictures taken by us show how Physarum

polycephalum was propagated in each situation.

a) b)

c) d)

Figure 12: Results of experiments: (a) for s = 0 and d = 0,

(b) for s = 0 and d = 1, (c) for s = 1 and d = 0, (d) for s = 1

and d = 1.

TowardsLogicCircuitsbasedonPhysarumPolycephalumMachines-TheLadderDiagramApproach

169

One can see the following cases:

• s = 0 and d = 0: uneventful, because there is no

data regardless of switch position,

• s = 0 and d = 1: no repellent causes the stream to

go to A

, the model does not grow down because

it is outside the region of inﬂuence of A

• s = 1 and d = 0: uneventful, because there is no

data regardless of switch position,

• s = 1 and d = 1: the repellent causes selection of

the lower path to A

It means that the Physarum polycephalum behaves as

intended.

6 SUMMATION

In the paper, we have shown how to construct ba-

sic logic gates in Physarum polycephalum machines

using the idea of ladder diagrams. Proper relation-

ships between ladder diagrams and Physarum poly-

cephalum computing have been pointed out. The pa-

per consists, in the ﬁrst step, in research connected

to developing a biological architecture of different

abstract digital devices based on the ladder diagram

principle. This principle is very popular in program-

ming Programmable Logic Controllers (PLCs). How-

ever, in case of PLCs, the ladder diagram principle is

used only at the abstract level as a high-level program-

ming language. The program is executed by silicon

microprocessors based on the standard architectures

not reﬂected in the direct ﬂow of power. Our approach

could allow a direct hardware implementation of this

principle in different controllers. In our case, it is a

biological hardware implementation.

The approach presented in this paper may be used

in different constructions of logic gates in chemical

media or on biological substrates which are based on

the ﬂow or propagation of some medium. An impor-

tant thing is to ﬁnd the mechanism of controlling the

ﬂow or propagation in the restricted regions by some

elements which can be activated or deactivated. The

main problem for the further work is to search for

mechanisms of constructing complex digital systems.

For example, in ladder diagrams, negations of com-

plex expressions must be realized using some internal

variables enabling us to carry states of coils to states

of contacts.

Another task for the further work is to implement

the presented idea in the experimental environment

for more complex circuits. In this case, an important

thing is the proper control over states of stimuli, i.e.,

their rapid activation or deactivation. Moreover, the

construction requires adjusting proper regions of in-

ﬂuences of individual stimuli to model serial or paral-

lel connections.

ACKNOWLEDGEMENTS

This research is being fulﬁlled by the support of FP7-

ICT-2011-8.

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