define the following relations...

sa, sr, wa, wr

which stand for "strongly attracts", "strongly repels", "weakly attracts" and "weakly repels", respectively.

algebraically, all four of these relations are symmetric, but not reflexive or transitive.

Let r be the distance between two centers c₁ and c₂, i.e. r=((x₁-x₂)²+(y₁-y₂)²+(x₁-x₂)²)^1/2

d²r/dt²=-2 if c₁ sa c₂

d²r/dt²=+2 if c₁ sr c₂

d²r/dt²=-1 if c₁ wa c₂

d²r/dt²=+1 if c₁ wr c₂

make sketches in your favorite CAD program of n of the following centers, assign random (x_i,y_i,z_i) coordinates to each of the c_i's, being very generous with spacing. Note that there are more attractive forces than repulsive forces listed below. Since the centers have size, include a mean radius r_i for each center. c_i and c_j should repel if dist(c_i,c_j)i+r_j, no matter what relation holds between the two centers. Next, run the simulation. The following are only a few examples to get you started.

bed sa toilet

bed sa shower.prep.ctr

shower.prep.ctr sa shower

shower sa clean.garment.ctr

interior.garage.door sa driver.side.car.door

clean.garment.ctr wa pantry

pantry sa kitchen

clean.garment.ctr sa dryer

dryer sa washer

washer sa laundry.tub

washer sa dirty.garment.ctr

dirty.garment.ctr sa interior.garage.door

bed sa fitness.ctr

fitness.ctr sa golf.net

dojo sa fitness.ctr

fitness.ctr sa shower

dirty.garment.ctr sr pantry

pantry sr toilet

pantry sa cooking.ctr

nuker sa cooking.ctr

range sa cooking.ctr

cooking.ctr sa recycling.ctr

recycling.ctr sa waste.ctr

waste.ctr sr pantry

pantry wr recycling.ctr

cooking.ctr sa dining.ctr

dining.ctr sa dirty.dishes.ctr

dirty.dishes.ctr wa waste.ctr

dirty.dishes.ctr sr pantry

dirty.dishes.ctr sa kitchen.sink

kitchen.sink sa dishwasher

dishwasher sa dish.storage.ctr

dish.storage.ctr sa dining.ctr

coat.rack sa front.door

mail.ctr sa front.door