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2011 January 03

A plethora of p4 hasslers

Scot Ellison has discovered a new p4 heavyweight emulator, with a different shape to the conventional one. Further, the two designs can be amalgamated to yield a hybrid emulator.

Scot Ellison's period-4 heavyweight emulators

Actually, this was not a completely serendipitous discovery; Ellison specifically designed his hybrid p4 to reduce the bounding box of Adam P. Goucher's p36 gun, by replacing the original (much larger) p4. That gun was itself a modification of Jason Summers' original 3-engine version.

Reduced period-36 gun

This modification allows a similar reduction in the size of the p108 gun, which is composed of two p36 guns.

Moreover, the p4 heavyweight emulator can be contracted to progressively form a middleweight, lightweight, and underweight emulator. Noam Elkies noticed the remarkable fact that the underweight emulator can push a traffic light predecessor, enabling the construction of a p32 hassler. David Buckingham noticed an alternative mechanism, which superficially resembles Elkies' oscillator, but can be reduced to a smaller, less symmetrical form.

Noam Elkies' and David Buckingham's p32 hasslers

Noam Elkies produced yet another p32 hassler, again based on the underweight emulator, but facilitating a completely different mechanism. A ship is used to remove two extraneous blinkers in the standard, Paleolithic way; Elkies suggests that it may be possible to coax a glider out of these blinkers in a similar fashion to the p24 gun. This monomer can be used as the basis of a p32 dimer, and Elkies postulates that a similar p36 dimer may also be possible. However, we already have a p36 gun (as mentioned earlier in this entry), so that would have limited use.

Period-32 monomer and dimer

Matthias Merzenich found a use for the middleweight variant of the hybrid emulator, replacing the p12 crown oscillators in the original p168 pi orbital. This modification is applicable to the p84 (168/2) orbital. Unfortunately, the successive copies of the pi heptomino cannot be packed closely enough to facilitate a p56 (168/3) orbital, as suggested by Noam Elkies.

Period-84 pi orbital using middleweight emulators

Additionally, he adapted one of the hasslers to enable the construction of a period-44 traffic light hassler.

Period-44 traffic light hassler, utilising a modified p4 sparker

Finally, David Buckingham found another use for the underweight emulator: to reduce the bounding box of the p124 'lumps of muck' hassler.

Reduced period-124 oscillator, by David Buckingham