lowest prices:
16K Static Memory Board
8K Static Memory Board
This 8K board is available in two versions. The 8KS-B operates at 450ns for use with 8080 and 8080A microprocessor systems and Z-80 systems operating at 2M Hz. The 8KS-Zoperates at 250ns and is suitable for use with Z-80 systems operating at 4MHz.
Both kits feature factory fresh 21 02's (low power on 8 KS-B) and includes sockets for aii iC's. Support logic is low power Schottky to minimize power consumption. Address and data lines are fully buffered and 4K bank addressing is DIP switch selectable.
Memory ProtecVUnprotect, selectable wait states and battery backup are also designed into the board. Circuit boards are solder masked and silk-screened for ease of construction. These kits are the best memory value on the market! Available from stock . . . 8KS-B $125 (assembled and tested add $25.00)
8KS-Z $145 (assembled and tested add $25.00)
Base 2 can now offer the same price/performance in a 1 6Kstatic RAM as in its popular 8K RAM. This kit includes 8K bank addressing with 4K boundary address setting on DIP switches. This low power unit provides on-board bank selection for unlimited expansion . . . No MUX board required. Using highest quality boards and components we expect this kit to be one of the most popular units on the market. Available in two speed ranges, the 1 6KS-B operates at 450ns while the 1 6KS-Z operates at 250ns.
16KS-B $285 (assembled and tested add $25.00) 16KS-Z $325 (assembled and tested add $25.00)
S-100 for Digital Group Systems
Z-80 CPU Board
Our Z-80 card is also offered in two speed ranges. The CPZ-1 operates at 2M Hz and the CPZ-2 operates at 4MHz. These cards offer the maximum in versatility at unbelievably low cost. A socket is included on the board for a 2708 EPROM which is addressable to any 4K boundary above 32K. The power-on jump feature can be selected to address any 4K boundary above 32K or the on-board 2708. An On-board run-stop flip-flop and optional generation of Memory Write allows the board to run with or without a front panel. The board can be selected to ru n in either the 8080 mode, to take advantage of existing software, or in the Z-80 mode for maximum efficiency. For use in existing systems, a wait state may be added to the M 1 cycle, Memory request cycle, on-board ROM cycle, input cycle and output cycle. DMA grant tri-states all signals from the processor board. All this and more on too quality PC boards, fully socketed with fresh IC's. CPZ-1 $1 1 0 CPZ-2 $ 1 25
This kit offers, at long last, the ability to take advantage of S-1 00 products within your existing Digital Group mainframe. Once installed, uptofour S-1 00 boards can be used in addition to the existing boards in the D.G. system. The system includes an
"intelligent" mother board, ribbon cables to link existing D.G. CPU to the DGS-1 00 board and a power wiring harness. The DGS-1 00 is designed to fit in the 5-3/4" x 1 2"
empty area in the standard D.G. cabinet. It may seem expensive but there's a lot here!
End your frustration! DGS-1 00 $295
bo1e 2. inc.
Circle 26 on i nq u i ry card.
Send for more details on these products. Get on our mailing list for information on more soon to be announced products at factory-direct prices from BASE 2. Why pay more when you can get the best at these prices???
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BYTE December 1978 63
Figure 7 4: A long period eater bound oscillator. This object has a period of 52; 7 3 gener
ations are required for 90 • of rotation. The central section is attacked twice by one eater each time it rotates.
Figure 7 5: A period 6 oscil
lator which employs the period 6 eater. This matching of period frequencies prevents the eater from disrupting the re
forming central group.
64 December 1978 © BYTE Publications Inc
is used, the patterns results in two blin kers, six blocks, and one tub in 1 1 0 generations.) Class I l l : Spaceships
Regrettably, there have been no new spaceships reported since the orthogonal spaceships presented in Scientific American in 1 971 . These are summarized in figure 1 6. other spaceships travel at c/2. The interest
ing th ing to note is that the three larger spacesh ips travel orthogonal ly. The ortho
gonal spaceships are most useful in several of the types of puffer trains to be d iscussed in the next section.
Class I V : Pattern Producing Mechanisms Class I V is divided into two sections: the
first contains static patterns that produce moving progeny, and the second contains moving patterns that produce some type of stationary or moving ou tput.
Spaceship Guns
The debris that would normally be removed by eaters col lides and just happens to create a gl ider that escapes without harming the shuttles. The period 30 glider gun is of paramount i m portance to simulations in Life and the possi ble existence of computing mechanisms. These impl ications wil l be d iscussed in a l ater article.
The period 46 gun, known as a newgun, also works by having two shuttles collide.
I t may be seen in figure 1 8. I n this case the shuttle consists of two B heptominos (described later) travelling opposite one another to produce debris at both ends of trails consisting of stationary objects. Leav
ing stable objects is useful when the inten
tion is to produce a train of puffers to build some sort of construction on the fly.
The three basic puffer trains all work
weight spaceships able to control the object;
the whole configuration puffs along at c/2.
This object reaches a stable period of 1 40 after a startup time of over 1 000 genera
tions. Additional spaceships may be added to the end of the object to further adjust the output from it in order to reduce the final period, the startup time necessary to reach a stable period and to adjust the output to blocks, gl iders, etc.
A type of puffer similar to the previous one is called a Schick ship {after its dis
coverer) . This is an i nteresting object {con
sult figure 20) in that the "engine" is real ly a tagalong, an object capable of being pulled along behind another object (usual l y a spaceship). Here, a heptomino follows a pair of m irrored spaceships. I t is quite remarkable that this configuration leaves a small trail of debris beh ind it and that, although this debris would die if left alone, additional spacesh ips fol lowing behind are able to trigger the debris into varying forms of static debris. The static debris can be left behind and used later. It is relatively useful for building armadas because of the relative simplicity of creati ng th is object from gliders (producing a basic ship requires 1 1 gliders).
The last type of puffer train is the smal l est, a mere 1 1 b its at startup - the size is somewhat larger when the fi nal repeat cycle is known, since there is transient debris in the field . This particular trai n travels very slowly, taking 96 generations to traverse eight spaces {speed c/1 2). I t is also very unusual in that it is the only known puffer train that travels d iagonally -.the same d i rection as the gl ider, but th ree times as sl ow.
U nl i ke the other puffer engines,' this train does not require that any other space
ship exist to bound it. To stabil ize the basic engine, a block must be placed somewhere in the debris produced by the object to prevent the debris from destroying it. I f the engine i s run without a stabil izing block, some risi ng debris final ly catches the engine after 1 1 fu ll cycles and destroys it. The remai ning field settles down to a fi nal census only after 391 1 generations !
Pertinent to the above paragraph is the fact that random patterns are quite often able to prod uce certain types of edge con
figurations, which enable them to surge forward with a great burst of speed for short periods of ti me. I n the case of the switch engine, when some random exhaust manages this type of movement, this slow movi ng engine is easily caught.
The switch engine (presented in figure 21 ) will produce, after its startup time, eight blocks every 288 generations. Other debris can be produced, including gli ders.
Since this train travels so slowly, there are presently no real uses for it.
a b c d
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0
Figure 7 6: The four known spaceships which occur in Life. Their appellations are: a, glider; b, lightweight spaceship; c, middleweight spaceship; and d, heavyweight spaceship. The glider travels diagonally at a rate of one space every four generations. The other three travel orthogonally at one space per two generations.
0 0
0 0 0
IOU 0 0 0 0 0 0 0
IUO OIV ::> 0 0 0 0
10 ::> 00 0 0 0· 0 0
0 0 0 0 0 0
0 0 0
0 0 0
Figure 7 7: This glider gun, which has a period of 30 generations, was the first object of class I Va to be discovered. It periodically emits a glider which travels away diagonally. The four block still fifes are used as eaters to dispose of debris. Glider guns are of great importance in simulations, where gliders are
made to collide, thus forming new objects. ·
u,u v,u u VIV
'-'I'-' IU v VIV
VIU v v VIO VIU
v u VIU
VIO VIU
10
1VIO v
1'-' v 10 IV
,v IV
IV v
v IO U
'
0 0 0 0
0 0 0 0
Figure 7 8: A period 46 glider gun which is called the newgun. Two twin bees shuttles collide at right angles to produce one glider every 46 gen
erations. A s before, the block still fifes are used to remove debris which could cause disruption of the formation.
December 1978 © BYTE Publications Inc 65
0 0 0 0 0 0
0 0 0 0
0 0 0 0 0
0 0 0 0
0 0 0 0 0
Figure 7 9: A puffer train constructed from the precursor to a B heptomino and two lightweight spaceships. A fter a startup period of over 7 000 generations. it stabilizes into a period of
7 40 generations.
Figure 2 7 : The switch engine puffer train, with a basic period of 96. A fter startup, it produces eight blocks every 288 generations after the initial stabilization of debris. A lthough much various debris may be created with this train, its slow speed limits its usefulness.
Figure 22: Several com
mon nonterminal random objects. These are desig
nated as follows: a, R pentomino; b, B hepto
mino; c, rr heptomino; and d, acorn. The acorn is a Methuselah type object.
Finding all the descend
David Buckingham is an undergraduate science student at the Univer
sity of Waterloo. 'He tnade a nurnber of contributions to the now defunct publication Lifel ine. Most of these had to do with o�tillators, which con
stitute his main field of interest in Life. He has at present found over 700 osc/1/ators of periods greater than two.
Buckingham s most productive area of research has been the devising of glider collisions to produce objects of classes I thru I V. As of August 7978, he has managed to create collisions to produce all of the presently known 7 7 05 objects of less than 7 5 bits in size.
66 December 1978 © BYTE Publications Inc
Class V: Random Objects some of the more com mon nonterminals and their names.
The most com mon object of this class must be the oft publicized R pentomino (figure 22a) , which many people still bel ieve runs forever. The result of th is pattern was, however, published in Scientific A merican ; it ru ns for 1 1 03 generations, prod uci ng heavily investigated objects, as is evidenced by some of the material presented i n th is article. It has the following interesting property : the front configuration of the object moves along to reappear the same every other generation, but fl ipped over.
A close relative of the previous object is th e rr heptomino (figure 22c) with a census of five blinkers, six blocks and two ponds i n 1 73 generations. Phase 1 of this object was cal led a blasting cap by the artificial i ntel l igence researchers at Massa
chusetts I nstitute of Tech nol ogy (M IT) ;
Early issues of BYTE carried a never completed series by Carl Helmers inad
vertently entitled "LIFE Line, " which was also the name used for Robert Wainwright's newsletter. These Helmers articles appeared as follows:
' ' L I F E Line 1 ," September 1 975 BYTE, volume 1 . number 1 , pages 72 thru 80;
" L I F E Line 2," October 1 975 BYTE, volume 1 , nu mber 2, pages 34 thru 42;
" L I F E Line 3," December 1 975 BYTE , vol ume 1 , nu mber 4, pages 48 thru 55;
" L I F E Line 4," January 1 976 BYTE, volume 1 , nu mber 5, pages 32 thru 4 1 .
A bibliography of Scientific American information on Ll FE (all references are to Martin Gardner's "Mathematical Games " column).
October 1 970: page 1 20. This is the origi nal Life article, including the defi n ition of the facts of Life, and i l l ustration of n u merous fundamental patte rns . November 1 970: page 1 1 8 . Answers to
several q uestions posed i n the fi rst
article on the subject, i ncl uding defi
nition of the several varieties of spaceships .
January 1 97 1 : pages 1 05, 1 06 and 1 08.
Continued progress o n the Life front i ncluding answers to several unsolved questions and results of a flurry o f computer Life activity.
February 1 97 1 : Special "Mathematical Games" article o n "cellular automata theory."
March 1 97 1 : pages 1 08 and 1 09. Short note about progress made by John Conway and R William G osper, plus ill ustration of a large scale fli p flop pattern which is deli cately balanced and easily destroyed by minor disturb
ances such as impact of a glider.
April 1 971 : pages 1 1 6 and 1 1 7 . Examples of fuses, the 5 cell cross series, and announcement of Robert T Wain right's Lifeline r)ewsletter.
November 1 97 1 : page 1 20. Short note on continued progress at the M IT A I Laboratory.
January 1 97 2 : page 1 07. The discovery of the eater by B i l l G osper at M IT.
Hurry down to your public library if you wish to use these references, as due to lack of space some local libraries may be committing the unspeakable crime of throwing away Scientific American . .. . CH
The january 1979 issue of B YTE will con
tain an artie!� by Mark Niemiec which · de-. scribes several a/go-, rithms for Life. Readers
who wish to experi
ment with Life patterns will find these algo
rithms useful in writing 1
efficient Life programs for their computers.
December 1978 © BYTE Publications Inc 67
Figure 7 : The state o f a cell in the next generation is computed from its pre
sent state and the states of the four other cells in its neighborhood. The neigh
borhood of a cell consists of all cells within a dis
tance of two cells from the cell in question.
(a}
D
(b)