‘Smart Surface’: Massively Parallel Actuator Array Controlled by NonLinear Medium. 
In order to simulate motion of the object on the ‘Smart Surface’, the object is divided into fragments as shown in figure below. Each fragment takes account of contribution from the cell underneath. The nature of force is depend on the type of microactuator used in particular practical realisation of ‘Smart Surface’ system. The various types of microactuator are discussed on the Hardware page. The simulations with the approach, where microactuators presented by microjets shown below.
A square divided into fragments.
1. Openloop model.
Model parameters and assumptions.
1. Type of microactuators—microjets; 2. Feed back from light sensors—no; 3. Size of lattice  100 x 100 cells; 4. Neighbourhood—8 adjacent cells; 5. Number of possible cell states—3 (refractory, excited, resting); 6. Mapping rules—stipulated by the excitation interval (Details in [1]); 7. Force between idle cell and object—no; 8. Force between excited cell (airjet) and object– proportional to the area of the fragment; 9. Direction of the force vector at the excited cell—depend on excitation in the neighbourhood; 10. Initial state of lattice– random distribution, 2% of refractory, 2% of excited cells with random force vectors; 11. Initial position of the object—in the centre of the lattice; 12. Tested objects—square 5x5, isosceles triangle, rectangle, octagon; 13. Simulation system of units—dimensionless.
Results of simulation.
Motion video clips.
Triangle travels down (AVI 4.7Mb); Triangle travels up (AVI 5.5Mb); Triangle stays in the middle (AVI 7.6Mb); Triangle receives impulse to the left (AVI 3.8 Mb); Triangle travels upright quickly (AVI 3Mb);
Square moves up with heavy spin (AVI 8.5Mb); Square travels up fast (AVI 3.1Mb); Square bounces between generators (AVI 8.5Mb); Square oscillates in the middle (AVI 9.0Mb);
Rectangle moves to the right slowly (AVI 7.6Mb); Rectangle moves down slowly (AVI 7.7Mb);
Analysis. For the triangle, square and octagon a statistical analysis of resultant trajectories has been carried out. To do this, 30 trials were made for each shape and mapping rule, starting from random lattice state. For every obtained trajectory some indices characterising its shape and length are calculated, namely 1. Trajectory length; 2. Trajectory inequality; 3. Furthest trajectory point; 4. Translational velocity of the object over trajectory; 5. Absolute rotational velocity
These indices are averaged over 30 trials and sketched against mapping rule for every object. Following picture shows the average trajectory length for triangle, square, octagon for various mapping rules. For further details refer to paper [1].

Trajectory length for the excitation interval [1,Theta2] 
Trajectory length for the excitation interval [2,Theta2] 
2. Closedloop model.
Model parameters and assumptions.
1. Type of microactuators—microjets; 2. Feed back from light sensors—level of cell illumination from 0 to 100; 3. Size of lattice  100 x 100 cells; 4. Neighbourhood—8 adjacent cells; 5. Number of possible cell states—3 (refractory, excited, resting); 6. Mapping rules—stipulated by the excitation and light sensitive intervals (Details in [2]); 7. Force between idle cell and object—no; 8. Force between excited cell (airjet) and object– proportional to the area of the fragment; 9. Direction of the force vector at the excited cell—depend on excitation in the neighbourhood; 10. Initial state of lattice– empty lattice; 11. Initial position of the object—in the centre of the lattice; 12. Tested objects—square 5x5, isosceles triangle, rectangle, octagon; 13. Simulation system of units—dimensionless.
Results of simulation.
Some results of simulation. 
Horizontal motion of a square on the lattice with light sensitivity interval [1,3] and excitation interval [1,8]. Red squares—excited cells, blue—refractory, white—resting. 
Motion of a square on the lattice with light sensitivity interval [4,4] and excitation interval [1,8]. Motion induced in the direction of displacement. After t=17 excitation does not occur. 
Example of drifting object in the field of target waves. In this case excitation propagates outside of the object via nonshadowed cells. Light sensitivity interval [1,2], excitation interval [1,8]. 