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2011 October 25

Beyond Herschels

If you asked a fellow Life enthusiast for the most important GoL discoveries in the 1990s, the Herschel track must surely feature. With a few elementary conduits, it is possible to design tracks capable of moving a signal to anywhere in spacetime (as long as there is enough 'manouevring room' and sufficient time), and placing it in any orientation. Herschel tracks underpin all but two of the known stable reflectors, and support the construction of glider guns for every period greater than or equal to 62.

Flow matrix for five common transient objects.

Firstly, what is so special about the Herschel? Is it really so much more useful than any other transient objects? It appears that the answer is both yes and no: other objects can be used, but they must eventually decay into Herschels. This is illustrated rather eloquently by a simple matrix. The row represents the input; the column represents the output. A red blob indicates if a primary (one-stage) conduit exists to transform the input into the output. Clicking on the matrix will enable you to download a complete collection of primary conduits. (A collection of all conduits, primary and composite, is provided later in this article.)

Guam's 309-generation left-turn conduit.

Some of these conduits are new discoveries. The Pi-to-R converter was discovered by Guam on the forums, published in the form of a quaternary Herschel conduit: H-Pi-R-B-H. The completed conduit takes 309 generations to turn a Herschel anticlockwise, so is designated L309. In terms of the number of intermediary objects, L309 is the most complex Herschel conduit to date. Indeed, its 309-tick delay is rather rapid for a quaternary conduit.

Isomers of Guam's 266-tick Herschel conduit.

Not content with a single new conduit, Guam proceeded to discover a pi-to-Herschel converter capable of attaching to a handful of 'pre-Herschel' conduits. Moreover, the symmetry of the pi heptomino means that Guam discovered not only one conduit, but two 'isomers'! The conduits are designated F266 and Fx266 for the translation and glide-reflection variants, respectively. However, the restrictions upon which conduits may follow F*266 severely limit its use in practical Herschel circuitry.

Matthias' tertiary Herschel conduit, the Lx496.

From an earlier posting of mine, you may remember the contributions of a certain 'MikeP', again from the forums. Matthias Merzenich has utilised a particular catalyst of his in a few conduits, including the periodic R135 conduit and a stable Pi-to-century converter. To process the resulting century, Matthias proceeded to find two unique century-to-Herschel converters, one of which is sufficiently compatible to yield a new tertiary Herschel conduit, the Lx496.

Matthias even found a use for this new inundation of Herschel conduits; he has incorporated them into glider guns with smaller dimensions than the current record-holders. Specifically, they are a p421 gun derived from the L309 and p685 gun based on the Lx496.

Guam's 4hd Herschel receiver.

In addition to his spectacular Herschel conduits, Guam also found two reactions in which gliders collide with constellations of still lifes to form extra junk. We already have a glider-to-beehive and glider-to-block converter, virtue of Paul Callahan, but we can now add loaves and bi-blocks to the collection. The latter is especially interesting, as a glider in the same direction as the original can liberate the bi-block in the form of a Herschel. The gliders are separated by 4 half-diagonals, unlike in previous receivers, where the separation must be 2, 5 or 6; hence, this new receiver could function where others fail. Also, it transpires that the bi-block functions as a LWSS eater, which can be toggled by incoming gliders.

Finally, he noted that two gliders separated by 4 or 5 half-diagonals can be reflected into a single glider. Here it is demonstrated as part of a stable reflector and related pulse divider. Alas, this reflector does not break any records, unlike the next subject of discussion -- the rectifier. This fast reflector, subject of a previous article on LifeNews, can be used in various conduits for transforming Herschels into gliders, by either modifying the output or assisting in the cleanup of surplus blocks.

To summarise this article, here is a collection of the 30 distinct Herschel conduits (including four adjustable ones), and a comprehensive collection of every (sufficiently simple) conduit, transceiver and converter known, as of the time of writing.

The article probably seemed long enough already, without the addition of an extended entry. After all, after concluding an article about Herschel conduits, why would anyone need an extended entry? What else is there possibly to mention? If we've covered everything at the sub-conduit level, one need only explore the cornucopia of possibilities unlocked by chaining conduits together.

Back at the forums, some Life enthusiasts have collaborated to compile a large, sprawling mass of stable reflectors and Herschel tracks into a clumsy HWSS Heisenburp device. Being the first of its kind, there are many optimisations one can make. I believe that the beastly bounding box of this Brobdingnagian behemoth can be reduced by an order of magnitude in area; I leave this as an exercise to the reader. Have fun!

The prototype HWSS Heisenburp.