Wikipedia:Reference desk/Archives/Mathematics/2017 April 25

= April 25 =

Cochleoid
How can I calculate Cochleoid? — Preceding unsigned comment added by 185.95.204.46 (talk) 14:52, 25 April 2017 (UTC)


 * See Cochleoid. Loraof (talk) 15:52, 25 April 2017 (UTC)

Broadcasting on a dynamic grid
We are given a nxn grid, where each node can maintain a single "active" edge with one of its 4 neighbors at each time step. The active edge of each node changes periodically clockwise or anticlockwise, in the sense that if, for example, at time t node v has an active edge with its upper neighbor, and it rotates clockwise, at times t+1, t+2 and t+3 it will maintain an active edge with its right, lower and left neighbors, respectively.

at time t=0 node (i,j) holds a message, and at each time step a node that has already received the message can transfer it through an active edge to one of its neighbors, if that neighbor also maintains this edge as active at this time step.

I am looking for sufficient conditions (initial active edges configurations and rotation direction of all the nodes) such that the message can be transmitted to all nodes in the grid.

Thanks! — Preceding unsigned comment added by 77.126.156.248 (talk) 17:20, 25 April 2017 (UTC)
 * If you just want a sufficient condition: every node rotates clockwise. The node at position (i,j) starts with the right edge active if i+j is even, and with the left edge active if i+j is odd.--2406:E006:2C7:1:1521:7BAE:223B:27D9 (talk) 03:09, 28 April 2017 (UTC)
 * That, or the three other rotations of it, is also a necessary condition. Dmcq (talk) 10:34, 28 April 2017 (UTC)
 * For entirely clockwise, yes. Once nodes are allowed to rotate either direction, there are continuum many solutions.--2406:E006:2C7:1:1521:7BAE:223B:27D9 (talk) 13:59, 28 April 2017 (UTC)