... A Moiré Story

Alpha Delta Epsilon Zeta

As first mentioned in The Basics-Part 2, we see a different moiré pattern and/or configuration in each of Wah's ten communicators:











To simplify the matter, though, all but two of the above were derived from only two separate original images; a painting called "Fall" and Edmund Scientific's "Pattern #4."  This is how it all came together.

Pattern #4 - The "Spider" Moiré

Dr. Gerald Oster (at far right, here w/ Salvador Dali), renowned bio-physicist and mathematician then with Brooklyn’s Polytechnic Institute, co-wrote a May 1963 Scientific American article on the optical effects of moiré patterns - the strange and interesting curvy lines generated from overlaying two similar (or identical) images atop one another.  In an effort to make his work more accessible, he then teamed up with Edmund Scientific Co. to create a whole range of moiré products and educational materials for mainstream consumption.

The initial cornerstone of this initiative, first offered in their 1965 catalog, as detailed on page 74:

(link to higher resolution image of page 74 for easier reading)

... was a "Student's and Experimenter's Moiré Kit" and similar "Educator's and Designer's Moiré Kit" (with thicker stock) of eight small patterns (3¾" x 4½" transparencies with matching cards).  This first set they came out with in 1965 was called their "Series (A)":

It also came with a reference book discussed more in detail below.  Of the eight moiré patterns Dr. Oster first created, the one that seems to have caught Wah Chang's eye most was Pattern #4 radial, which when rotated atop each other creates a wonderful "spider" effect of expanding and contracting circles.  When turned by a 30 second stopwatch, this became the dynamic effect in his two hero communicators.  The image below is of an actual transparency/card; the red lettering is our:

The distance the stacked images are offset influences the resulting moiré arc lines.  Here with Pattern #4, observe that the closer the two centers are, the fewer but thicker are the lines, and the closer to the center the arcs can still be distinctly seen:

The second (1/8") and the fourth (1/32") pics above approximate what we see in Alpha (0.107" offset) and Beta (0.035" offset), respectively:

The exact offset distances we quote were derived from reproducing the moiré patterns seen in the screen caps with an authentic Edmund kit Pattern #4 and determining the center-to-center length with a measuring loupe.

The appearance of the moiré pattern is not the only difference between the two heroes.  In Alpha the entire pattern rotates every 30 seconds, while in Beta it remains at a stationary angle.  If you put the center of the bottom (turning) layer off the axis of rotation (the stopwatch shaft), thus having the top motionless transparent layer on-center, the arcs will grow and shrink as always, but in addition the entire pattern will rotate at the same speed and direction as the stopwatch.  However, if the bottom layer is on-center with the top being off-centered, the growing / shrinking arc patterns will stay fixed in the same orientation.

This difference can be seen by drawing a line through the arc axis of both.  In "Friday's Child," Alpha's pattern rotates in the 4.5 second total clip about the expected 54 degrees.  In Beta's one open close-up in "Day of the Dove," during about 2.5 seconds (starting while the camera is still zooming in) we would expect 30 degrees of rotation if it was built identical to Alpha, but instead there is no rotation...

Alpha beginning:    ending:         Beta beginning:    ending:

Now if both top and bottom layers are off-center, then the arc patterns will transition from a slow many-arc pattern like Alpha to a fast few-arc pattern like Beta and back again.  We actually see this happening in the large moiré display next to Spock's bridge station:

While we have multiple good images of Alpha that show a consistent pattern throughout its 30 second rotation (thus proving the top layer is centered, as confirmed by the modern physical examination of the very prop), it remains a possibility that Beta's two layers could both be off-center with a fluctuating pattern like that on the bridge above, simply because we only see this one comm up close only once and for such a short period of time.  We'll have to find it to know for certain.

*   *   *   *   *   *

With the #4 pattern established as his hero model, Wah looks to have scrounged for extra similar images to put in some of his eight static dummies, so he turned to a related source.  To accompany Edmund Scientific's moiré kit, Dr. Oster  also wrote a short technical guide book called “The Science of Moiré Patterns,” copyrighted 1964 and selling for $2 at the time:

front    back

The pink seen on the cover of this first (1964) edition is on a plastic overlay held on by the bright red "report" clip on the bound edge.  All pages of this 8.5"x11" book are reproduced at the bottom of this page for your studying pleasure.

On its page 9 we see a number of moiré patterns reproduced.  The #4, while much more crude here on rough paper stock than on the smooth Kromokote, was nonetheless cut out and installed in Epsilon.  Note the asymmetric blank patch surrounding the black dot in the center that confirms for us the exact source and also its rotational orientation in the prop:

Wah next cut out the Pattern #4 "spider" image from a loose-sheet advertising insert (a reprinting of a combined page 38 and 74 from the Edmund Scientific catalog) that came along with the 1964 moiré book - and put it into Kappa:

Our pages had previously said that Wah cut Kappa's "spider" from an actual 1965 catalog.  He did not.  A pristine fully-intact 1964 "The Science of Moiré Patterns" book was found to have an enclosed advertising insert that was an exact full-sized reproduction of the '65 catalog's pages 74 (which had the "spider") and 38.  Here are both possible sources, side by side:

The ad insert was printed on the same rough-surface matte paper as the moiré book, rather than the smoother glossier magazine stock the catalogs used, resulting in a little blurring of the image's sharpness and a less saturated blackness to the ink.  Also the ad insert had some imperfections - tiny patches of missing ink - that allows today a 100% positive match to the Kappa outtake image.  So for those of you who obtained Edmund catalogs for your Kappa replica comm, your pattern will be the exact same image size-wise, but a tiny bit darker and crisper to what actually went into Wah's version.

*   *   *   *   *   *

Starting in 1966, Edmund sold an expanded line of Dr. Oster moiré product kits which included extra moiré patterns, some in larger image sizes and colors.  This 1966 catalog had the exact same page 74 as the 1965.  It also had the "spider" on the cover, but that one is too large by about 25% to match what went into Kappa:

(link to higher resolution image of page 140 for easier reading)

It is apparent that Wah wanted to mix things up a little, so he switched over to another pattern for four other comms...

Fall - The "Wavy" Moiré

We begin this part of our tale in 1963 with world-famous British abstract artist Bridget Riley (right), who that year painted amongst other eye-twisting geometric pictures a large 55 in. x 55 in. canvas she named "Fall" - now hanging in the the Tate Britain Museum in London:


A year later, the afore-mentioned Dr. Oster observed the retinal-scrambling properties of Ms. Riley's work.  To accompany his own patterns in his first (1964) edition of “The Science of Moiré Patterns,” he had printed her piece on the front and back covers, plus on page 24.

Each of the three "Fall" images (cover, page 24, and back) is at a different scale, which allows us - by matching wavy lines seen in screen caps and other photographs - to determine exactly which ones Wah Chang used.  Even more specifically, since “Fall” was hand-painted, slight variations in line widths can be seen that allows us to identify the precise location within that image they were cut from!  So from the image appearing on Dr. Oster's book cover, Wah scribed for certain two circles (using an old-fashion radial compass that poked a hole at the center), cut them out and inserted them into his communicator props we now know as Delta and Iota:

Delta is self-explanatory; the wavy lines in modern photos being an absolute perfect match to the Moiré book cover - right down to the fraction of a millimeter.  For Iota we must use a slightly less-precise method.  The individual lines can't bee seen, but the pattern can still be located by observing the secondary "bunching lines" formed from the linear clumping of tight waves.  These larger lines have their own spacing to each other, plus lighter and darker regions within, that allow us to get within hopefully a few millimeters of the actual center.  More on Iota's here.

Another easy one... from page 24 Wah cut a circle for Gamma, and the great TMOST photo plate allows us to zero in on the exact location:

Regarding the "why" of this wavy pattern, we can only guess that Wah found the lines reminiscent of an oscilloscope, thus looking high-tech with a certain dynamic movement induced even while standing still (when looking at the whole painting, it really does jump around and boggle the eyes).  However, we'll never know why Wah chose two "Fall" images, or why he cut two circles from the cover, whose lines were so thin that Delta's and Iota's pattern could never be seen on a television screen.  In fact, only once in an episode, in Assignment: Earth (r >>), were the individual lines in a wavy pattern (Gamma's) at all evident.  It can be imagined that first Wah was inspired by the cover of Dr. Oster's book and began cutting, then maybe found the bigger image of "Fall" later on page 24.  If so, apparently Wah never bothered to re-cut more circles from the page 24 (and arguably better) image and just used what he had already trimmed.  Perhaps he glued them into the bezels as he went along and didn't want to rip out what he had previously completed.

Moving on for a while from the wavy patterns...

A "Gun Barrel" Spiral for Eta's Moiré

For some reason Eta got almost no airtime whatsoever.  Just a few hard-found distant glimpses inside are all we've got to go on:

What stands out is the white patch at the center.  Very distinct.  Within The Science of Moiré Patterns book, there are two patterns that are a close match, and so previously we figured it could only be either of these; the Pattern #7 "Fresnel" concentric circles (printed right on the same page 9 where Wah cut the images out for Epsilon's and Zeta's), and another even-cruder representation of the Pattern #4 radial from page 1 (at right in order >>).  Both, however, look to have a larger white center than screen caps suggest.  Might there be other options?

Yes.  Another possible source within the pantheon of Edmund Scientific products had just become available at the time.  A year after they first offered their "Series (A)" Patterns #1 thru 8 moiré patterns / transparencies in 1965 came their second, lesser-known "Series (B)" kit of Patterns #11 thru 18:

Pattern #18, technically called a "30-line logarithmic spiral," though perhaps more familiar as the James Bond movie opening-credits gun barrel, also has a resemblance to screen caps of Eta.  It just so happened to have been used in the very first replica made after the show's cancellation (at right >> courtesy of TPZ member SGT) by a small fledgling operation called Starfleet Fabrications, some of whose members had visited the set during production and may have seen original comms in action to base their later builds on.  This possible connection, and the pattern they used, could be mere coincidence... but perhaps not.

In our considering Wah's hypothetical use of the Series (B) set, it should be noted that no other dummy comm uses a pattern cut from any of the kit cardstock/transparencies (of course he had at least two Series (A) kits to make the two hero models.)  All other identified patterns came from the cover, inside pages or advertising insert of the Science of Moiré Patterns book, so the #18 spiral, appearing at the proper size ONLY on the thick Kromokote cardstock and plastic transparencies from the (B) kit, would represent a significant departure from norm.  It would also assume that Wah actually had this second, less common set of patterns, for which there is no prior firm evidence.

So the best way to choose amongst these three potential candidates is to line them up and see which one looks the closest.  We do this by enhancing the screen caps and then comparing them to appropriately-blurred digital images of the patterns:

Nothing above reveals anything firmly conclusive, but the size of the center white patch along with the absence of darker rings or black dots heavily leans our opinion towards the #18 spiral.  There is indeed enough visual evidence here to suggest Wah had the Series (B) set of patterns.  As odds makers, we give the #18 a 75% likelihood, whereas the #5 Fresnel is at 20% and the #4 radial 5%.

A New Source for Theta's 2-Layer Moiré

Theta's has been a surprisingly tougher call still.  Sure, we have found a few screen caps of the insides that should allow a straightforward enough identification.  However, we see in these a paradox that we've been struggling with for years.  When on the floor in Bread and Circuses (its best appearance), the moiré is dark with a couple of vague diagonal black streaks (except around the bottom where it looks like an obscuring glue smear).  But the only other three inside views from elsewhere in the series seem to reveal a near total absence of any features whatsoever.  Just blank light grey:

What's going on here?  There certainly is no single image printed on paper that can be both dark and light at the same time.  So which is it?  If you just start with the clips above and crank up the contrast, you can coax out the consistent hints of two parallel lines (easier to see in the first, sort of there in the others) that have a similar spacing as the bunched wavy lines of Iota, but a whole lot lighter:

Here we have the faint suggestion of "Fall" waves, but certainly not from the cover of the moiré book (which sourced Delta and Iota).  Again, those printed bunch lines are dark and stand out with ease.  Fortunately there is another source of that picture that is the same scale but much lighter.  It happens to be on the same ad insert that Kappa's pattern came from, and thus we believe a circle cut from there went into Theta:

Why then the note above about the added transparency?  To account for the afore-mentioned paradox.  This paper image cannot create the dark moiré region seen only in the B&C floor shot, with the messy glue stain at the bottom standing out prominently there alone.  What this puzzle strongly suggests is that Theta has a top plastic layer, which reflected the dark background as seen there on the floor.  In the others it reflected a brighter costume, skin or set.  So might this plastic have a pattern of its own like the hero moirés?  Maybe, which could explain the extra fuzzy dark patches as per the B&C floor shot.  Or maybe not, because it would add darkness to the overall pattern not necessarily evident in the other screen caps.  We cannot tell with any certainty either way.  50-50.  If the transparency does have a pattern, it would have to be very light, like this simple black dot screen that came on the cover of the 1965 edition of The Science of Moiré Patterns book.

Editor's Note (Feb. 2010)  If you've been keeping up with our site, you know we've changed our opinion about what's in Theta's moiré since Day One.  Back and forth it has gone.  This newest find and evaluation confidently brings us much, much closer to satisfying all known criteria.  So with no more data to study, the topic should be wrapped.  That is, until the actual prop shows up.

Non-descript uniform Concentric Circles for Zeta's Moiré

For Zeta he oddly plucked the Pattern #5 (a boring evenly-spaced 34 lines per 1/2" radius).  It is a blessing that this particular dummy comm survived, as it did not appear even once open throughout the entire series; thus we wouldn't have had a single clue otherwise as to its moiré pattern or other inside details:

This concentric circle pattern is duplicated nearly exactly on the front cover as well, but the quality of the print there (the cover having a rougher line smoothness) tells us with absolute certainty the source for Zeta is Page 9.  Now, when you look on the back of that moiré ring (>>), you don't see the printing on the reverse page that should there.  It looks like Wah cut the circle too small and glued it to another disk, perhaps (based on the color) from a common manila folder, with a larger diameter for securing in the ring.  It is not known if all other dummies had a backing layer.  Pattern #5 also came in a transparency/card combo in the moiré kit just like Pattern #4, but its paper surface is smooth and shiny; not a match with what's in Zeta:

The lines in this pattern are so small that except for WAY up close, they instantly blur into a uniform 50% grey patch.  Why Wah would have selected an image with features much too tiny to ever possibly show up on a TV screen, or why he didn't put the stylus of the protractor in the bull's-eye center point of the pattern, will forever unknown.  Note that Zeta's moiré bezel is now loose from the shell, so the original orientation is also a guess (unless Mr. Jein took a photo of the prop prior to his dismantling it).  That of course hasn't stopped us from taking a stab, and based on a VERY crude matching of glue spots on the ring vs. what's left on the shell, we show a modestly uncertain off-angle orientation in our simulation at the top of this page and in the print-ready 1200 dpi version.

It will also be an enduring mystery as to why precisely Wah didn't use more of the transparencies and cards that came in the two moiré pattern kits he had, other than what he probably did in Theta.  Many of those pattern combinations create interesting images even when not being rotated, and the shiny top surface would at least match his heroes.  However, the apparent glue mishap on Theta, where the stuff looks to have seeped all over the place (obscuring part of the image) may be the likely answer there.  Too much trouble.

*   *   *   *   *   *

All Pages of the 1964 "The Science of Moiré Patterns" Book

For those who wish to explore further the actual book Wah used as the pattern source for all eight static dummy communicators, we provide the following scans of all twenty eight pages, plus the outside and inside of both front and back covers as well as the advertising insert (for Kappa's pattern), at 150 dpi resolution.  Wah cut out circles from the front cover (for Delta, Iota and maybe Theta), from Page 9 (Epsilon and Zeta) and from Page 24 (Gamma).  Those page names are highlighted in red for a quick find.

Front Cover outside

Front Cover inside (blank)

Page 3

Page 4

Page 5

Page 6

Page 7

Page 8

Page 9

Page 10

Page 11

Page 12

Page 13

Page 14

Page 15

Page 16

Page 17

Page 18

Page 19

Page 20

Page 21

Page 22

Page 23

Page 24

Page 25

Page 26

Page 27

Page 28

Page 29

Page 30

Back Cover inside

Back Cover outside


Advertising Insert (front)

Advertising Insert (back)
All Cards from the original "Series (A)" Edmund Scientific Co. "Experimenter's Moiré Kit"

Sold in the mid 1960s alongside the above moiré science book, and also utilized by Wah in his two hero communicators, was the Moiré Experimenter's Kit - Deluxe.  Those kits that had Patterns #1 through #8 were called their "Series (A)."  It contained eight 4½" x 3¾" Kromokote (a museum-grade semi-gloss white stock) cards, each with a different pattern and a matching transparency.  The description in quotes is what Edmund named each.  We have provided here scans of all eight cards at 300 dpi resolution.  The "Deluxe" version of the kit simply had thicker transparencies (0.020") than the standard version (0.005") and slightly heavier cardstock.  Wah of course used two Pattern No. 4 in his hero comms (Alpha and Beta).  Maybe he also had #3 as the top layer on Theta.

Pattern No. 1
"Coarse grating"

Pattern No. 2
"65-line grating"

Pattern No. 3
"Logarithmic scale grating"

Pattern No. 4
"Radial lines 5º"

Pattern No. 5
"Equispaced circles"

Pattern No. 6
"Fresnel zone plate"

Pattern No. 7
"Sphere projection"

Pattern No. 8
"Cylinder projection"
All Cards from the "Series (B)" Edmund Scientific Co. "Experiment's Moiré Kit"

Starting the following year (in 1966), after the success of the "Series (A)," came the "Series (B)" kit with Patterns #11 through #18.  It is likely Wah used the #18 in Eta, but none else are known to be used in any other comms.  For those who are curious, Edmunds did not ever print a Pattern #9 or 10.  Maybe this was just to line up the second number sequence 11-18 with the first one 1-8.

Pattern No. 11
"Coarse sines"

Pattern No. 12
"65-line sines"

Pattern No. 13
"Perspective squares"

Pattern No. 14
"Medium grating"

Pattern No. 15
"Gaussian grating"

Pattern No. 16
"Converging circles"

Pattern No. 17
"Elliptical zone plate"

Pattern No. 18
"30-line logarithmic spiral"


Some Cautionary Notes about Sourcing

Two subsequent editions of Dr. Oster's book, from 1965 and 1969, are of limited or no use to us...

The 1965 and identical 1966 versions, which have a grey printed plastic overlay above the cover instead of pink, does not have the "Fall" image on the cover (the only differences between the 1964 and the 1965 editions), and thus is missing the patterns for Delta and Iota:

The completely revised 1969 version, with a full-color front cover, has no authentic images left in it at all.

None of these books contain Pattern #4 transparencies.  Edmund Scientific, which was sold to new owners in the 1990s, offers today another moiré book written by a different author, and while it contains a #4 in a transparency (it does not have a corresponding #4 on paper), the quality of the image in its center is again poor and not recommended for use in hero replicas.


Downloadable 1200 dpi images of all actual patterns used can be found on the Parts and Plans page for the Moiré and Moiré Bezel. moire

Star Trek is a Registered and Copyrighted Trademark of Paramount Pictures.  All Rights Reserved.  All subject matters referring to Star Trek are trademarks of Paramount Pictures.

This website has not been produced or endorsed by Paramount Pictures.  Any material belonging to Paramount’s Copyrighted Material that may appear on this site complies with fair and/or acceptable use for the purposes of review, study, criticism, or news reporting.