6 cells, 43 and 50 generations
I found 11 unique (up to reflection) 6-cell solutions:
By the first generation of evolution, they form two identical groups:
The first, fourth, and last two patterns work by the same method as my previous answer, but are three generations (one pulsar period) slower. Except for some self-destructing debris they are the same ...
6 cells, 111 generations
I found 12 unique (up to reflection) 6-cell solutions:
They all work by the same method as my previous 8-cell solution, forming a house one cell below the top of the base area at generation 6. Here's an animation:
There are no solutions with fewer than 6 cells (that stabilize within 200 generations).
previous solution: 8 cells, ...
23 cells, 41 generations, humorous answer
Sorry, I couldn't resist it... The pulsar dies on "magical command" after 41 generations but it takes 23 initial cells.
I apologise for the crudeness of the image. It's my first time using Golly.
EDIT: The next challenge is answered under my registered name Ruutsa
I have a solution:
I shamelessly stole the upper part from BaSzAt's 8-cell sun destroyer, and, by trial and error, found a 7-cell lower part that generates a new pulsar without interfering with the upper half. Like BaSzAt's solution, it takes 44 steps to gobble up the old sun, although the new one is already fully formed after 32 generations. The center ...
In case anyone is wondering, here is my own solution, which takes 38 generations.
(NB: When I made this puzzle, I had no idea if it's even generally solvable. It took me 4 or 5 hours, while having the freedom to change the drawing area as I like.)
By the way, the bottom cells are just for decoration. The following works too:
Here is my answer in text form. It's long, so I stored it on pastebin:
I don't have time to convert it to png (thanks @TheDarkTruth, see comments to the question), so maybe later.
Gif animation :
19 cells, 41 generations, another humorous answer
EDIT: Only just noticed my answer to the previous challenge was logged in under the guest name user21465.
Continuing in the vein of humorous answers, here's another one. I thought it was going to be difficult and when I tried it I said ...
Here's the animation
Not exactly answering this question, but given 9 infections still on an 8x8 board, it is actually possible to delay the inevitable until 40 days. Pretty counter-intuitive huh?
Locations are A1, A5, A8, B3, B7, D1, E8, G1, H8
Also, I believe that this is the maximum for an 8x8 board with any number of initial infections.
As for the edges argument I made ...
The nonincreasing quantity $X$ to look at this time is
Pattern code to verify in a CA simulator such as Golly:
x = 9, y = 9, rule = B45678/S012345678
EDITED - thanks to @Meelo for pointing out my mistake.
We can do it in
We place the C.Coli's at a4, a8, b2, c1, e2, g1, h3, h6.
Now we prove that this is optimal. Every day there are either 1 new infected cell or 2+ new infected cells. Let us have k days with single infections and l days with 2+ infections. Then k+2l<=56 and therefore k+l<=28+k/2. ...
This is by no means an answer, but using @2012rcampion's interpretation, I wanted to illustrate how this fractal can be generated using top-down approach, starting from a single element:
/ \/ \
/ /\ \
/ / \ \
\ / \ /
/ \/\/\/ \
\ /\/\/\ /
The element is ...
Here's a 17-cell solution that works at any distance:
I bet this (or something very similar) is the solution you were expecting. It consists of:
This solution takes 2×n + 32 steps to destroy the target, where n is the number of rows between the starting area and the target oscillator. In your baseline puzzle, n = 7, so the target is destroyed in 46 ...
A .rule file, for Golly users, provided by AxiomaticSystem
Further features of this cellular automaton beyond the questions posed here, including new spaceships, a puffer and rakes that generate gliders, racers, and swimmers, are in this thread at the Conway Game of Life Wiki.
Phoenix 1: (added by Jeremy Dover)
Beacon and Clock: (...
Twenty virus samples are necessary. A chessboard can be divided into two diagonal meshes with no diagonal adjacencies between them, and the virus can't spread from one to the other just like a bishop can only reach half the squares, so we can consider only the "black" squares and use the same pattern for the white. Furthermore, if we rotate the board 45 ...
Consider the diagonals going northwest/southeast. (I'll call these primary diagonals and the ones going the other way secondart diagonals.) Look at the top-right-most primary diagonal that contains any alive squares. None of those squares can survive, since they can have at most one cell alive in their neighborhood. This means that in each step with living ...