and y (vertical)-directions. Also consider a particle in this doenain whose sise is equal to a cell siare. Thestore. if we assume that ibe length of a cell is 1 unit, then the borizontal and vestical components of the particle's speed mary be 1,0 or 1 , separastly. Figare 1, Powible trajecories of a particle at each sapp. The boundaries of te domata ise insumed in be solld surfacm therefore of a particle bin a boundary it will reflect from the boundary (see figure 2). The amow in the figury which the particle would move to at the ne's time step. There may be more than ose particle in the domain and these particles may collide wal rock odter. The collicion is assumed to be filly thistic. If the two particles are denoet with 1 and 2 and thrir The above relations would be applied only when the two particles ase in the serictborise crilk. Noe either be 1 cer 0 . You are expected to develep a Martlaboctave program which would place four particles in the would have an initial velocity which is assigned randonily. The velociry of the purticles would remain constant unell they collide with each other or hit the botmderies of the domaie The above relations woold be appled only when the two particles are in the reighorang cells. Note that when the two particles are in neighboring cells ahsolute value of x1x and (y1yn) can eiller be 1 or 0 . Yoe are expecind is develop a Martaboctave progam which would place fout partickes in the domain at random poxitions. (Na reo particies slould be at the same position). There particles would have an initial velocity which is assigned randonly. The veliocity of the particles would remain constant undil dery collibe with rach other or hit the boundaries of the doeain: Your proegam is to simulate the motion of the particles as a function of tine. For this purpose the partices would be presented with square symbols on an sy-plot and the position of a particle will be updaird accosting tor Where the time nsp A4 is equal to 1. After de positions of the particles are updaind the fipure should be updated alwa. Note that there should be only one fipure showing the cument powitions of the particles. The simulation should be mast for 100 time steps. You may consider ining the "pause" tunction for bener visualizacion. Recording be positions of the particles, your program should create a vecond figure which plets the trajectories of the particles. The program should alwo write the sy positions of particles as a function of yinie in is texe files as a table with suicable column heriders. The total displacemeat of the particlefhould also be wrinen ae the eid of the tile. Bua of each particle will be wrinten in sa a differes tife. esplanutices. The peocram mav contain a main script and user-detined.f.finctions