# Herschel conduit

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A Herschel conduit is a conduit that moves a Herschel from one place to another.

Well over a hundred simple stable Herschel conduits are currently known. As of the end of 2017, the number is approximately 130, depending on the precise definition of "simple" -- e.g., fitting inside a 100 × 100 bounding box, and producing output in no more than 300 ticks. In general a Herschel conduit can be called "simple" if its active reaction does not return to a Herschel stage except at its output. A description of common usage in complex circuitry, using syringes and Snarks to make compact connections, can be found in Herschel circuit.

Herschel conduits can be chained in order to form a Herschel track. Karel Suhajda's search program Hersrch automates the process of building a track.

## The original universal set

The original universal set consisted of sixteen stable Herschel conduits, discovered between 1995 and 1998 by Dave Buckingham (DJB) and Paul Callahan (PBC); these are shown in the following table. In this table, the number in "name/steps" is the number of ticks needed to produce an output Herschel from the input Herschel. "m" tells how the Herschel is moved (R = turned right, L = turned left, B = turned back, F = unturned, x = flipped), and "dx" and "dy" give the displacement of the center cell of the Herschel (assumed to start in the orientation shown to the right).

Name/steps m dx dy discovery
R64 R -11 9 DJB, Sep 1995
Fx77 Fx -25 -8 DJB, Aug 1996
L112 L -12 -33 DJB, Jul 1996
F116 F -32 1 PBC, Feb 1997
F117 F -40 -6 DJB, Jul 1996
Bx125 Bx 9 -17 PBC, Nov 1998
Fx119 Fx -20 14 DJB, Sep 1996
Fx153 Fx -48 -4 PBC, Feb 1997
L156 L -17 -41 DJB, Aug 1996
Fx158 Fx -27 -5 DJB, Jul 1996
F166 F -49 3 PBC, May 1997
Fx176 Fx -45 0 PBC, Oct 1997
R190 R -24 16 DJB, Jul 1996
Lx200 Lx -17 -40 PBC, Jun 1997
Rx202 Rx -7 32 DJB, May 1997
Bx222 Bx 6 -16 PBC, Oct 1998

The initial universal set of Herschel conduits is shown below, proven to be sufficient to complete an unlimited range of synchronization or computation tasks. Many more Herschel conduits have since been discovered. Conduits are code-named according to the final orientation of the output Herschel relative to the input Herschel, and the number of generations it takes for the output Herschel to reach the same phase as the input Herschel. For example, the R64 conduit performs a right turn in 64 generations; "R" designates right turn, "L" left turn, "F" forward motion, "B" backward motion and "x" flip ("forwards" is defined as along the shaft towards the T-piece).

• For conduits for symmetrical inputs (e.g. a pi-heptomino or queen bee), an asterisk (*) is used to denote that the conduit can be flipped to place the input either clockwise or counterclockwise. The resulting pair of conduits will have outputs in the same number of ticks, but they will be either F and Fx (F*), L and Rx (L*), R and Lx (R*), or B and Bx (B*).[1]
• As shown below, the conduits transport the input Herschel (shown in green) to the position in magenta, and also produce a glider which escapes at lower left.[2]
• The two Bx conduits leave a block (shown in red) which has to be deleted by the glider produced by the output Herschel.
• In F166 and Lx200 the "input Herschel" never actually forms in the position shown, which is given to facilitate the concatenation of conduits. Instead, the block and Herschel-precursor react as shown in the insets, 3 generations before the nominal entry into the conduit.
• The number in brackets is the reset time, i.e. the minimum number of generations at which one Herschel can follow another through the conduit. However it may be necessary to dispose of the glider produced by the output Herschel to achieve some close spacings.
 R64 (61) Fx77 (57) L112 (58) F116 (138) F117 (63) Fx119 (60) Bx125 (166) Fx153 (60) L156 (62) Fx158 (176) F166 (115) F171 (227) Fx176 (92) R190 (202) Lx200 (90) Rx202 (201) Bx222 (271)

Many of these use the block+snake combination (Conduit 1) in order to clean up the output B-heptomino to produce an output Herschel. Dave Greene, with the invention of his boojum reflector, discovered a way to remove this block using the first natural glider of the Herschel. However, these conduits are not considered 'elementary', since they contain a boojum reflector.