Clock-Driven Pattern
Two three-cell bars flipping at the same rate, in the same colour, side by side. One is computed by a rule. The other is painted by a routine that never looks at the grid. Watching them will not tell you which is which.
The left grid works out its next frame by counting neighbours. The right grid is wiped and redrawn every tick by something outside it, and nothing in that routine ever reads what is on the grid. They are built on completely different principles and they look the same. Motion is not evidence of anything. To find out which grid is doing the work you have to interfere with it, and this page is about what that test costs and what it turns up.
On this site a basin is the set of conditions a system comes back from. Push a marble around the inside of a bowl and it rolls back to the bottom; the bowl is its basin, and the rim is its edge, the push beyond which it does not come back. Finding basins, and their edges, is the point of the Laboratory. This is a caution: coming back after a disturbance does not by itself prove a basin. Of the two bars here, the one computed by a rule makes its own blink, and the panel found no disturbance it comes back from. The painted bar comes back every time and has no basin at all.
| basin | what it returns to | what pushes it | its edge |
|---|---|---|---|
| 1. The computed blinker | its own two-phase blink, three cells in a row, then three in a column | Scribble on both, or one cell scrambled near the centre | at the bar itself: from a one-cell scramble it came back 0.0% of the time |
1. The computed blinker. The left grid works out each frame from the last by Conway's rule, the Game of Life, in which each cell lives or dies by counting its eight neighbours. Under that rule a row of three becomes a column of three and back again, so each phase of the blink produces the other. That dependence on its own state is real, and it reaches almost nothing beyond the bar. The panel scrambled one cell near the centre in 2,000 trials and ran each forward for up to twelve ticks: the blinker came back 0.0% of the time, died out 43.9%, and became something else 56.1%. The edge is the bar itself: no disturbance tested here brought it back.
The painted bar has no basin. It comes back 100% of the time from a one-cell scramble, in one tick, and also from a five-cell scramble and from a completely random grid. Press Scribble on both and wait one tick: the painted grid is clean and the computed grid still carries the damage. The painted bar recovers because a routine outside the grid wipes it and redraws the bar where its own counter says, every tick, and that routine never reads the grid. It would come back just as reliably if the bar were a smiley face. The program supplies the return, so the return says nothing about the bar.
Stop the clock is not a push. It freezes both grids, which any paused program does, and tells you nothing about either.
Same Motion, Different Reasons
Stopping the Clock Proves Nothing
Press Stop the clock. Both grids freeze. That is the whole result, and it is worthless, because pausing a simulation pauses it. The Lorenz attractor stops when you stop stepping it too. Freezing on command is a property of programs, not of the thing being simulated.
It is worth being blunt about this because the earlier version of this page was built on exactly that test, and claimed from it that a blinker’s motion was “imposed by an external tick, not produced by the configuration”. That is backwards. Run the identical clock over a Game-of-Life block instead of a blinker:
The clock decides when the rule runs. The configuration decides what happens. A blinker blinks because three cells in a row become three cells in a column under Conway’s rule, and no clock can make a block do that.
The Test That Works
Press Scribble on both. The same three cells are flipped in both grids, so immediately afterwards the two look equally damaged. Wait one tick.
The painted grid is clean. Its routine wiped the whole grid and drew the bar where its own counter said, exactly as it does every tick, and the scribble was never consulted because nothing in that routine consults anything. The computed grid is still carrying the damage, and from here it will do whatever Conway’s rule says to do with six cells in that arrangement, which is usually to die.
The grid that is doing no work is the one that shrugs off the interference. It is immune precisely because it is inert: a thing that never reads its own state cannot be disturbed by a change to it.
The Number That Should Worry You
Scramble one cell at random and run each grid forward. Two thousand trials:
| comes back | dies out | becomes something else | |
|---|---|---|---|
| computed by the rule | 0.0% | 43.9% | 56.1% |
| painted from outside | 100% | 0% | 0% |
The painted stripe returns from a one-cell scramble every single time, in one tick. It returns from a five-cell scramble every time, from a completely random grid every time, from any state you can put it in. On the face of it that is the most robust object on this site.
It is also the only object here that computes nothing. The recovery is a routine redrawing a bar, and it would recover exactly as reliably if the bar were a smiley face.
So “it comes back when you disturb it” is not by itself evidence of a basin. Perfect recovery is what you get from a system with no dynamics at all, and the blinker beside it, which has real dynamics, recovers from essentially nothing. Before a recovery counts for anything you have to know whether the thing recovering is reading its own state. That is the claim this node exists to make, and it is a caution about every other basin on this site rather than a fact about blinkers.
Why This Is an Attractlet
The painted grid is the plainest supplied structure in the set. Every frame is written by something outside it and it contributes nothing, not even the rule. Stop the routine and there is no pattern, no recovery and no object.
The computed grid is supplied too, though less obviously. Conway’s rule and the clock that applies it both come from outside; the grid contributes the state and nothing else. What it does have is a genuine dependence on its own configuration, which is why interfering with it does something, and that dependence is the only difference between the two halves of this picture.
What This Model Is Not
The scramble is local. Cells are flipped in the five-by-five square around the centre, not anywhere on the grid. A scramble far from the bar would leave the blinker alone and report a recovery that means nothing.
Twelve ticks is the horizon. A pattern that would have returned to a bar on the thirteenth tick is counted as “something else”. In Conway’s rule small perturbations settle or die within a few ticks, so the horizon is generous, but it is a choice.
One starting pattern. The card for this node used to promise “the starting patterns that settle into the same two-phase blink”, which the old panel had no way to show and this one does not show either. There is one seed. The claim has been taken off the card.
Moore-8, deliberately. The classical Game-of-Life neighbourhood, as the Block uses. It is a highly anisotropic substrate and that is appropriate for an attractlet that leans on its grid.
Gardner, M. (1970). The fantastic combinations of John Conway’s new solitaire game “life”. Scientific American, 223(4), 120–123.