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Here is a sawtooth spaceship based on a restartable boatstretcher and Corderships.


#C A diagonal sawtooth spaceship with a minimum population around 1760.
#C This uses a restartable diagonal c/4 boatstretcher and several
#C diagonal c/12 period 288 Cordership rakes and sparking Corderships.
#C ...

This is a slight advancement from my previous post of a year and a half ago. (I just took my original object and added a rake to act on the blocks to produce an irregular output stream.)


#C A pseudo-random rake based on PI crawlers.
#C This uses some period 36 c/2 puffers to create trails on ...

Which sawtooth has the slowest expansion rate?


Well, anchored patterns behaving like binary counters have pretty slow expansions.

For example, the logarithmetic growth pattern seen here:
https://conwaylife.com/forums/viewtopic.php?p=173130#p173130
is slowly expanding but at the same time quick ...

Here is an orthogonal sawtooth spaceship which is only the second instance of a sawtooth which uses the mechanism of creating an eater object at the front end which consumes spaceships sent by the back end. (The previous sawtooth using this mechanism was diagonal and used Corderships and a c/5 ...

The 'Line ship' LifeWiki article could have some additional information (worded much better than this).

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The original line ship shown above extends the growing line continuously at the front. This means that if the line is burnt from the trailing end and is not stopped, then the line-building ...

I figured out how to create the period doubling gun needed for the lineship sawtooth!

Here is the working sawtooth.


#C A sawtooth based on a Cordership line-puffer and a caber tosser.
#C The caber tosser emits gliders at generations 51072 * 2^N.
#C Its output and a few preceding gliders ...

I recently said in the sawtooth thread that there was no known glider gun which emitted gliders at an exact exponential rate. Happily, I was mistaken due to a confusion of the origin for counting the generations for the gliders in Cordership loops.

Dean Hickerson built the first caber tosser in ...

The 'Growing spaceship' LifeWiki article could mention that arbitrarily slow-growing spaceships are known based on a glider traveling back and forth between two trails of boats created by Cordership puffers.

BCNU,
-dbell

Continuing from my previous post, I rearranged the boat puffers in the slowly growing spaceship so that their rakes do not cross through a
boat trail to reach the other one. This means that the separation of the boat trails can be simply adjusted.

Here is a slowly growing spaceship showing the new ...

For years now I have been trying to make a sawtooth from the Cordership-based line ship. This is still unsuccessful, but recently I made a small amount of progress.


#C A Cordership-based line ship being ignited several times by gliders
#C which are separated from each other by 1596 * 2^N cells ...

A growing spaceship. Front is 16c/40, back is 8c/21. This means that the rate of growth is 8c/20-8c/21=2c/105. Is that the slowest so far?


That growth rate of 2c/105 is 0.019c.

An old boat-consuming Cordership pattern can be modified to create a slowly growing spaceship. All that is required ...

https://conwaylife.com/wiki/P1_megacell


The p1-megacell is impressive, but it doesn't quite meet the requirement.

I want a Unit Cell which is totally stable. The p16777216 gun in the p1-megacell disqualifies it, even though it is just a small part of the whole object.

I think it should be ...

Here is a new record adjustable period sideways rake.


#C An adjustable diagonal c/12 rake with a population of 333 cells.
#C This uses three two-engine Corderships. The back Cordership
#C converts a beehive into a forward glider. The top right
#C Cordership tries to duplicate the forward glider ...

I think it should be possible to build a new Unit Life Cell without any oscillators or guns.

That is, each Unit Cell is a completely stable object, except for the possible presence of a glider which indicates that its state is currently alive.

That glider is replicated to be sent to the ...

Using one wing of that three-engine Cordership combined with a different wing yields a three-engine Cordership with a minimum population of 132 cells vs. 139 cells. This gives a new 'proper' variable period rake with a minimum population of 381 cells.


The Cordership at the bottom of the ...

There are at least two ways that a glider can be cleanly deleted by a lobster. These two ways are very similar (the lobster is just advanced by one generation in the second one).


#C A glider is deleted by a c/7 lobster spaceship.
x = 30, y = 26, rule = B3/S23
17boo$16boo$17bobboo$15bo4boo$$16b3o ...

Does anyone know of an efficient algorithm using HashLife to find all of the cells of on object which lie on just one side of an oblique line connecting two points?

Currently, I have to do this by scanning the cells of the object one by one and checking each point against the line. This obviously ...

I have finished the cleanup of the oblique sawtooth spaceship. Hopefully I have not made a mistake in the construction since it is so hard to run it fully.


obliquesawtooth2.zip


There was a third fuse ignition mode that I missed in my previous posting. All three ignition modes are shown here ...

I have almost created the first oblique sawtooth spaceship. This is pretty large so I had to make an attachment.


justaboutsawtooth.zip


This has slope 1/2 and is made from several copies of the period 1024 hbkcaterpillar and the period 12 bi-block fuse puffer.

I found a tweak for the ...

Here is a possibly new slide gun reaction. Unlike previous slide guns, it pushes an object just one cell forwards instead of the usual two cells.


#C Three spaceships push a beehive by one cell and emit a glider.
#C A MWSS and a LWSS turns a beehive into a mango while emitting a glider.
#C A third ...

I thought someone might be interested in how I improved a feature that I had in my Life program. This might be useful for people to use in their own HashLife implementation.

One of the commands in my program is 'mm', which means mark the parts of the object which are king-wise connected to the ...

Does anyone have any c/3 or c/4 orthogonal block puffers that only emit a single chain of blocks?


I don't know what block spacing you require, so I made a collection of many different spacings.


#C Some simple c/3 and c/4 block puffers.
x = 1474, y = 239, rule = B3/S23 ...

I created a couple of "glider hasslers".

These are based on one-time turner reactions for a glider such that the turned glider reaches the same column as it started (and is flipped), and the reaction can be repeated if the bait object is recreated.

Here is the mechanism for the first reaction ...

Inspired by the recent infinite glider hotel by EvinXL, I built a new one which runs at maximum capacity.


#C A symmetric infinite glider hotel with two insertion points.
#C
#C The name is derived from the old mathematical "infinity hotel"
#C scenario, where a hotel with an infinite number of ...

Is there a way that a slash character can be considered as part of a word when searching?

For example, if I search for "c/4" the results look for "c" and "4", and complains that they are common words.

Adding single or double quotes doesn't help.

BCNU,
-dbell