Difference between revisions of "Sawtooth 177"
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'''Sawtooth 177''' is a refinement of [[Sawtooth 181]] obtained by rephasing the constituent guns. It is the smallest known sawtooth in terms of its minimum repeating population of 177. A bounding-box-optimized variant, Sawtooth 195, has a repeating population of 195 and a bounding box of 62×56,<ref>{{cite web|url=http://www.conwaylife.com/forums/viewtopic.php?f=2&t=1590&p=24382#p24384|title=Re: Smaller sawtooth|author="thunk" [pseudonym]|date=October 31, 2015|accessdate=October 31, 2015}}</ref> significantly smaller than the previous 79×55 record set by [[Sawtooth 201]]. By removing the 2 gliders, making all the | '''Sawtooth 177''' is a refinement of [[Sawtooth 181]] obtained by rephasing the constituent guns. It is the smallest known [[sawtooth]] in terms of its minimum repeating [[population]] of 177. A bounding-box-optimized variant, Sawtooth 195, has a repeating population of 195 and a bounding box of 62×56,<ref>{{cite web|url=http://www.conwaylife.com/forums/viewtopic.php?f=2&t=1590&p=24382#p24384|title=Re: Smaller sawtooth|author="thunk" [pseudonym]|date=October 31, 2015|accessdate=October 31, 2015}}</ref> significantly smaller than the previous 79×55 record set by [[Sawtooth 201]]. By removing the 2 gliders, making all the [[block]]s [[pre-block]]s, and making the pentadecathlon 10 cells in a row, it is possible to make a sawtooth that has 152 cells, but the minimum repeating population is still 177. | ||
The sawtooth functions by letting two glider streams of period 120 retract a block, created by collision with a spark from a [[58P5H1V1]], one cell at a time. The retracted block is deleted via interaction with a [[pentadecathlon]], and the streams are allowed to return to the now-farther-away 58P5H1V1 to create another block. | The sawtooth functions by letting two [[glider]] streams of [[period]] 120 retract a block, created by collision with a [[spark]] from a [[58P5H1V1]], one cell at a time. The retracted block is deleted via interaction with a [[pentadecathlon]], and the streams are allowed to return to the now-farther-away 58P5H1V1 to create another block. | ||
==Population== | ==Population== |
Revision as of 12:07, 4 October 2019
Sawtooth 177 | |||||
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Pattern type | Sawtooth | ||||
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Number of cells | 177 | ||||
Bounding box | 74 × 60 | ||||
Expansion factor | 121 | ||||
Discovered by | thunk | ||||
Year of discovery | 2015 | ||||
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Sawtooth 177 is a refinement of Sawtooth 181 obtained by rephasing the constituent guns. It is the smallest known sawtooth in terms of its minimum repeating population of 177. A bounding-box-optimized variant, Sawtooth 195, has a repeating population of 195 and a bounding box of 62×56,[1] significantly smaller than the previous 79×55 record set by Sawtooth 201. By removing the 2 gliders, making all the blocks pre-blocks, and making the pentadecathlon 10 cells in a row, it is possible to make a sawtooth that has 152 cells, but the minimum repeating population is still 177.
The sawtooth functions by letting two glider streams of period 120 retract a block, created by collision with a spark from a 58P5H1V1, one cell at a time. The retracted block is deleted via interaction with a pentadecathlon, and the streams are allowed to return to the now-farther-away 58P5H1V1 to create another block.
Population
The population is equal to 177 at generations 0, 3360, 409920, 49603680, ..., 28 * (121n - 1), ..., giving an expansion factor of 121.
References
- ↑ "thunk" [pseudonym] (October 31, 2015). "Re: Smaller sawtooth". Retrieved on October 31, 2015.