WWW page for the paper:  Is Bosco's Rule Universal?
Kellie Michele Evans
California State University, Northridge

The constructions described in the paper Is Bosco's rule universal? are presented here as java applets using the software MJCell written by Mirek Wójtowicz. Let us describe the java applets, all of which may be viewed in real-time by clicking on the "Start MJCell" button below.

Applets and their descriptions:

A.mcl: Bosco, the period 166 oscillator for which the rule is named.

B.mcl: A collection of bugs supported by Bosco's rule. The speed for each bug appears to its left. As the rule updates, the speeds disappear without affecting the bugs' trajectories.

C.mcl: One speed 5/6 orthogonal bug is turned into (1) a new copy of Bosco, (2) a speed 5/6 orthogonal bug, and (3) a speed 8/16 diagonal bug. Two additional copies of Bosco then transform the Bosco and the speed 8/16 diagonal bug into speed 5/6 orthogonal bugs, heading west. The reaction thus turns and triples the original speed 5/6 orthogonal bug.

Gosper.mcl: The first glider gun supported by Life and constructed by William Gosper.

D.mcl: The first bug gun supported by Bosco's rule and constructed by Dean Hickerson.

E.mcl: A period 332 bug gun.

F.mcl: Period 332 bug gun with a 90 degree turn and two spatial shifts.

G.mcl: A 6-bug salvo pulls a block 10 units.

H.mcl: A 5-bug salvo pushes a block 10 units.

I.mcl: Test for zero. In the applet, a block is pulled from "position 1" (10,0) to "position 0" (0,0) by a 6-bug salvo and the output from a period 332 bug gun is annihilated in the process. If the block had instead been pulled from any position greater than 1 or pushed from any position 0 or greater, the output of the period 332 gun would have moved south unharmed.

J.mcl: The shotgun, which creates the 11-bug salvo consisting of both the 6-bug pull salvo and the 5-bug push salvo. The applet requires a 2,300 by 1,100 lattice. Due to MJCell's spatial limitation of 800 by 600 lattices, it must be viewed using the full blown MCell, which is freeware available for download here. The experiment is contained in the file J.mcl, available for download here. Applets J1.mcl-J6.mcl illustrate the pieces of the shotgun described in the paper as follows:

   J1.mcl: Period 166 guns g3, g4, and g5 along with period 332 gun G created bugs b3, b4, and b5.

   J2.mcl: Guns G11 and G2, which have period 332 along with a turn and spatial shifts, create bugs b11 and b2.

   J3.mcl: Guns G6 and G9, which have period 332 along with a turn and spatial shifts, create bugs b6 and b9.

   J4.mcl: Guns G8 and G7, which have period 332 along with a turn and spatial shifts, create bugs b8 and b7.

   J5.mcl: Gun G1 which has period 332 along with a turn and spatial shifts, creates bug b1.

   J6.mcl: Gun G10 which has period 332 along with a turn and spatial shifts, creates bug b10.

K.mcl: Period 332 guns GA, GB, and GC, of the push suppressor create bugs A, B, and C, repsectively, which annihilate all 5 bugs of the push salvo. The 6 bugs of the pull salvo remain unchanged.

L.mcl: Period 332 guns GD, GE, and GF, of the pull suppressor create bugs D, E, and F, repsectively, which annihilate all 6 bugs of the pull salvo, without harming the 5-bug push salvo.

M.mcl: Push signal. The gun G in the southeast corner sends an external push signal, b_push, every 332 time steps. This bug is turned and duplicated by a control device, consisting of three copies of Bosco (B1, B2, and B3) and the new bugs, b_B and b_C annihilate bugs A, B, and C of the push suppressor.

N.mcl: Pull signal. The gun G furthest west sends an external pull signal, b_pull, every 332 time steps. This bug is turned and tripled by a control device, consisting of nine copies of Bosco (B4-B12); the new bugs, b_D, b_E, and b_F annihilate bugs D, E, and F of the pull suppressor. Due to MJCell's spatial limitations described above, N.mcl must be viewed using MCell. It is available for download here. Applet N1.mcl illustrates N.mcl as follows:

   N1.mcl: N.mcl is rotated 90 degrees in the clockwise direction to create this applet.

O.mcl: This is the system test for Bosco's Sliding Block Memory. It starts with 20,460 live sites on a 3,000 by 1,500 lattice. Due to MJCell's spatial limitation described above, the experiment, O.mcl, which is available for download here, must be viewed using MCell.

In order to view the applets, press the button below to start MJCell. When the applet window appears, make it as large as possible. Click on "Favourites," and the "Favourite patterns" dialog box will appear with all of the applet names described above. Click on the desired applet, press "Load," and the initial state will appear. In most cases, it is necessary to click several times on the "-" button that appears southwest of the figure (to zoom out). Press "START" to see the applets update in real time. Detailed documentation for MJCell appears here, along with a collection of other MJCell applets not related to this paper.