One Random Walker

<?xml version='1.0' encoding='UTF-8'?>
<MorpheusModel version="4">
    <Description>
        <Title>OneRandomWalker</Title>
        <Details>Full title:		One Random Walker
Authors:		L. Edelstein-Keshet
Contributors:	Y. Xiao
Date:		10.05.2022
Software:		Morpheus (open-source). Download from https://morpheus.gitlab.io
Model ID:		https://identifiers.org/morpheus/M2003
File type:		Main model
Reference:		L. Edelstein-Keshet: Mathematical Models in Cell Biology
Comment:		A Random walker in 2D: a cell is started at the center of the domain. At fixed time increments, the walker changes its direction of motion. Its velocity vector is then recomputed as a vector with random x and y components. A bias in the move direction can be introduced by setting BiasOnOff to 0 (Off) or 1 (On). Thanks: Uses some aspects of example RunAndTumble (Morpheus Model ID: M0025, https://identifiers.org/morpheus/M0025) provided in Morpheus.</Details>
    </Description>
    <Global/>
    <Space>
        <Lattice class="hexagonal">
            <Size symbol="size" value="200, 200, 0"/>
            <Neighborhood>
                <Order>1</Order>
            </Neighborhood>
            <BoundaryConditions>
                <Condition type="periodic" boundary="x"/>
                <Condition type="periodic" boundary="y"/>
            </BoundaryConditions>
        </Lattice>
        <SpaceSymbol symbol="space"/>
    </Space>
    <Time>
        <StartTime value="0"/>
        <StopTime value="10000"/>
        <TimeSymbol symbol="time"/>
    </Time>
    <CellTypes>
        <CellType class="biological" name="Walker">
            <VolumeConstraint target="200" strength="1"/>
            <ConnectivityConstraint/>
            <PropertyVector symbol="move_dir" value="0.0, 0.0, 0.0"/>
            <PropertyVector symbol="displacement" value="0.0, 0.0, 0.0"/>
            <PropertyVector symbol="velocity" value="0.0, 0.0, 0.0"/>
            <PropertyVector symbol="BiasDirection" name="spatial cue direction" value="0, 1.0, 0.0"/>
            <Property symbol="BiasOnOff" name="Turn cue on (1) or off (0)" value="0.0"/>
            <Property symbol="run_time" name="run duration" value="5.0"/>
            <Property symbol="last_turn_time" name="last random event" value="0"/>
            <DirectedMotion direction="20*move_dir+BiasDirection*BiasOnOff" strength="1"/>
            <Event trigger="when-true" time-step="5" name="Change direction">
                <Condition>time >= last_turn_time+ run_time</Condition>
                <Rule symbol-ref="last_turn_time" name="Time of last random event">
                    <Expression>time</Expression>
                </Rule>
                <VectorRule symbol-ref="move_dir" name="new direction of motion">
                    <Expression>rand_uni(-1,1), rand_uni(-1,1) , 1</Expression>
                </VectorRule>
            </Event>
        </CellType>
        <CellType class="medium" name="medium"/>
    </CellTypes>
    <CPM>
        <Interaction>
            <Contact type1="Walker" type2="medium" value="4"/>
            <Contact type1="Walker" type2="Walker" value="10"/>
        </Interaction>
        <MonteCarloSampler stepper="edgelist">
            <MCSDuration value="1"/>
            <Neighborhood>
                <Order>1</Order>
            </Neighborhood>
            <MetropolisKinetics temperature="0.6"/>
        </MonteCarloSampler>
        <ShapeSurface scaling="norm">
            <Neighborhood>
                <Distance>2.5</Distance>
            </Neighborhood>
        </ShapeSurface>
    </CPM>
    <CellPopulations>
        <Population type="Walker" size="1" name="Random Walker">
            <!--    <Disabled>
        <Cell id="1" name="1">
            <Nodes>100,100,0</Nodes>
        </Cell>
    </Disabled>
-->
            <InitCircle number-of-cells="1" random_displacement="5.0" mode="random">
                <Dimensions radius="10.0" center="100.0, 100.0, 0.0"/>
            </InitCircle>
        </Population>
    </CellPopulations>
    <Analysis>
        <Gnuplotter time-step="200" decorate="false">
            <Terminal name="png"/>
            <Plot>
                <Cells value="cell.id"/>
                <CellArrows orientation="20*velocity" center="midpoint" style="1"/>
            </Plot>
        </Gnuplotter>
        <Logger time-step="10">
            <Input>
                <Symbol symbol-ref="cell.center.x"/>
                <Symbol symbol-ref="cell.center.y"/>
            </Input>
            <Output>
                <TextOutput/>
            </Output>
            <Plots>
                <Plot time-step="5000">
                    <Style line-width="1.5" style="lines"/>
                    <Terminal terminal="png"/>
                    <X-axis>
                        <Symbol symbol-ref="cell.center.x"/>
                    </X-axis>
                    <Y-axis>
                        <Symbol symbol-ref="cell.center.y"/>
                    </Y-axis>
                    <Color-bar>
                        <Symbol symbol-ref="time"/>
                    </Color-bar>
                </Plot>
            </Plots>
        </Logger>
        <DisplacementTracker time-step="10" name="data" celltype="Walker"/>
        <ModelGraph format="svg" reduced="false" include-tags="#untagged"/>
    </Analysis>
</MorpheusModel>