Zoetrope Strip Maker

Line the inside of a bowl with twelve drawings of a bouncing ball and spin it. Nothing bounces. The drawings run together into a grey band, because at every instant each part of your eye is being shown a different one. The pictures are all there. What is missing is a reason to see them one at a time.

A zoetrope supplies the reason with cardboard. The drum has a ring of narrow slits above the strip, and you look through them at the pictures on the far side. Most of the time a solid wall is in the way. As one account puts it, the scanning of the slits keeps the pictures from simply blurring together. The toy is a machine for not looking.

What a glimpse is made of

Take one slit and follow it. For a moment it lines up with your eye and the wall behind opens. A short time later it has moved on and the wall is solid again. During that moment the strip on the far side was moving too, but only a little, so the drawing is caught almost still.

Then the next slit arrives. If there is one slit for every picture, the strip has travelled exactly one picture’s width in between, so the second drawing sits where the first one was. Nothing has changed place. Only the drawing is different. Twelve glimpses later the drum has turned once and the ball has bounced once.

That is the whole mechanism, and it is arithmetic before it is perception. A drum that turns once a second with twelve slits gives twelve pictures a second. Spin it twice as fast and you get twenty-four. The count of slits times the turns per second is the frame rate of the toy.

Researchers who built a variant of the drum for a perception study describe what happens inside one glimpse with a useful phrase: the parts of the figure are not on the retina at the same time but one after another, the image painted onto it as the figure passes the slit. Their drum had eight slits, each 4 mm wide, and turned at 150 revolutions a minute, which by the same arithmetic is twenty glimpses a second.

The explanation that would not die

For more than a century the standard account of all this was persistence of vision: each image lingers on the retina for a moment and blends into the next. It is still the phrase most people reach for. It deserves care, because the film scholars Joseph and Barbara Anderson took it apart in 1978 and again in 1993, and their argument is simple enough to check at the kitchen table.

If images merely lingered and blended, they write, the result would be a piling up of pictures, a static collage of superimposed stills, not movement. Blending is what the bowl without slits already does. They separate two questions that early writers ran together. One is why a flickering light looks steady, which the literature calls flicker fusion. The other is why a series of still pictures looks like motion, which it calls apparent motion.

The second question has its own history. In 1912 Max Wertheimer showed two lines one after the other and varied the gap. At the right timing observers saw one line travel, now called beta movement, or a pure sense of motion with no object, called phi. He concluded that processes behind the retina were needed. Both terms are still in use: Wikipedia’s article on the phi phenomenon sets the objectless kind against beta movement, in which the figures themselves seem to move. The Andersons add that swapping in the word phi as a new slogan explains no more than the old one did.

So the honest summary is this. The dark gaps between glimpses can fuse into a steady view if they come fast enough, and one modern study set its test lamp to 65 flashes a second as a rate people generally see as steady, while finding thresholds that differed between healthy adults by roughly 30 flashes a second. The movement itself is the visual system reading small shifts between successive pictures as motion. How it does that is still a research subject.

Three machines, one trick

The first of these toys was a disc. The Science Museum Group’s copy of the first phenakistoscope disc is dated 1832 and credited to the Belgian physicist Joseph Plateau. Drawings sit around the disc and slots are cut near its edge. You hold the printed side toward a mirror, spin it, and look through the slots at the reflection. The slots that ration your view are on the same disc as the pictures, so one person watches at a time.

The drum came next. The same museum records that the idea was first suggested in 1833 by the Austrian scientist Simon Stampfer, and William Horner published a cylinder with slits between the pictures in January 1834. It was not sold widely until 1867, after a design that put the slits above the pictures and let the strips be swapped. Its advantage was social: several people around a table could look through different slits at once.

The third machine removed the slits altogether. Emile Reynaud’s French patent of 1877 places flat mirrors on a polygon at the centre of the drum. The patent’s own geometry is precise: the mirrors stand at half the radius of the pictures and turn with them, and each picture is then seen at the centre. An 1879 article in La Nature describes a prism whose diameter is exactly half that of the box. The museum’s example has a drum 12.5 cm across.

With mirrors, one picture replaces the next without any shutter. The association that keeps Reynaud’s papers credits this with better visibility than the slotted toys. The museum calls it possibly the earliest moving picture shown without intermittent motion.

The numbers on one strip

Here is a strip worked through, with figures the tool on this page will reproduce. A drum 150 mm across inside has a circumference of pi times 150, so the strip is 471.24 mm long. Twelve frames share it equally, 39.27 mm each. A sheet of A4 is 297 mm long, so the strip will not fit in one piece; it prints as two runs of six frames with a glue tab between them. Letter paper, 279 mm long, splits it the same way.

Now the slits. Make each one 8 percent of a frame wide, which is 3.14 mm. A point on the far wall is visible only while the line from your eye to it passes through that gap, and both walls are moving, in opposite directions. Worked through for an eye 300 mm from the drum, the point travels 1.88 mm while it can be seen. That is the smear. Move the eye closer and the smear grows toward the full width of the slit. The same geometry makes every picture look about 60 percent as wide as it was drawn, which is why figures in a drum look thin.

The price is light. A slit that is 8 percent of the spacing passes 8 percent of the light. Widen it and the picture brightens and smears in step. There is no setting that gives both, and that trade is the reason for the mirrors.

Change the count of slits and something else happens. With thirteen slits for twelve pictures, each glimpse comes a little early. The next picture has not quite reached the place of the last, and it falls short by one thirteenth of a frame. After a full turn the shortfalls add up to one whole frame, so the picture creeps backward against the spin while it animates. Eleven slits make it creep forward.

A disc follows the same rules with angles. Twelve frames get sectors of 30 degrees, and each drawing is turned 30 degrees more than its neighbor so that all of them stand with their feet toward the hub.

Closing the loop, and filming it

A strip has no first frame once it is glued into a ring, so the last drawing must lead into the first. A ball that lands where it started closes by itself. A walk needs a whole number of steps. Where an action cannot return, playing the frames forward and then backward will always close.

A camera is a shutter too, and it can stand in for the slits. Cameras record at set rates: film settled on 24 frames a second, and video standards are built around rates close to 25 and 50 in most of the world and close to 30 and 60 in North America and Japan. If the disc advances exactly one picture between exposures, the film shows a still, animated picture: twelve frames filmed at 30 a second need 2.5 turns a second, which is 150 revolutions a minute. A little faster or slower and the picture drifts, by the same sum as the extra slit.

One caution belongs here. Flashing can trigger seizures in people with photosensitive seizure disorders, and the web accessibility guidelines draw their line at three flashes in any one second period unless the flashing area is small. A loop of strongly contrasting frames shown at twelve pictures a second can be well past that, in the hand and on a screen.

There are also things a calculation cannot promise. It treats the eye as a point and the paper as having no thickness. It cannot know whether a printer scaled the page, which is why a ruler is printed on every sheet. And a screen preview draws only as many frames a second as the screen has, so it cannot show the dark between glimpses. The cardboard will.