1. Formation of an ant cemetery: swarm intelligence or statistical accident 報告者 : 王敬育

2. Abstract The model of artificial ants is proposed by Deneubourg in 1991 。 1.pick & drop 2.swarm intelligence A new model with: 1.less intelligence 2.clustering can be explained by a statistical effect 3.the cemetery formation is not a collective phenomenon

3. Deneubourg ’ s model The key steps are the pick up & lay down phases: the probabilities K 1 ， K 2 are the parameters (K 1 = 0.1 ， K 2 = 0.3 ) f : a fraction representing the number of corpses memorized by the ant along its own path 。 f = N / T N: the numbers of items that encountered in the path T: the last T motion steps (T = 50)

4. The minimal model Pick up and deposition rule (1)Each time an unloaded ant sees a body on one of its eight neighboring cells ， it loads it with probability 1 。 If there are several bodies ， it chooses one of them 。 (2) After the ant has moved at least one step away ， the corpse is released provided the ant is surrounded by one or more dead bodies in its eight-cell neighborhood 。 If this is the case ， the ant deposits the body in a randomly chosen empty neighboring cell 。

5. The minimal model (3) Contrarily to Deneubourg ’ s model ， our ants never walk on a corpse 。 (maybe trapped in the cluster) Displacement rule (1)The ants move one cell at a time ， but heading in the same direction for a pre-assigned random number of steps 。 (the steps we call free path) After the number of steps ， the ants select at random a new direction of motion among the eight possible lattice directions and a new length for the next free path 。

6. The minimal model (2) The free path is chosen uniformly from the set {1,2,3 … L} ， independently for each ant 。 (in this model L = 100) (3) When a corpse lies on the trajectory of the ant ， a new random direction is selected as well as a new free path length 。 (4) To deal with obstacles: an ant which faces a blocking sit chooses a new direction of a new direction of motion and a new free path length 。

7. Result and comparisons What is the mechanism that biases the dynamics so as to form only one large cluster? In Deneubourg ’ s model: from the intelligence of ants In minimal model: the dynamics is biased towards forming larger clusters ， because : (1) small ones are more likely to disappear under statistical fluctuations (2) clusters cannot build up from nothing

8. Cemetery formation with heterogeneities

9. Dynamics of the formation process The process scales as: N( t ) = F(M t ) N( t ) : the number of clusters at time t simulation M: the number of working ants in the simulation F: some unknown universal scaling function depending on the details of the model