DIY · Card 60 · Art · Perception
Trace your hand, then draw nothing but lines across the page, each one arching up as it crosses the outline. Thirty lines later, your hand seems to rise right out of the paper.
01The brief
Make a flat drawing stand up off the page.
0
vanishing points, shading tricks or perspective rules needed
~30
lines, each straight, then arched, then straight
1
simple rule: lift each line by the height of the hand below it
Lay a ribbon across your hand and look at it from the side: it runs flat along the table, climbs over your knuckles and drops back down. Draw that ribbon, and a dozen more like it, and you have drawn the shape of your hand without drawing the hand at all.
That is the whole trick behind this famous illusion. It needs only a pencil, some felt tips and half an hour, and it uses the same idea as contour maps and 3D scanners. Like the moiré patterns and the missing square puzzle, it shows how easily simple lines can fool the eye.
02Kit
A pencil, paper and a few markers. And a hand.
Tick off what you have
0 of 3 ready
03Method
Straight outside the outline, arched inside it. That’s the whole rule.
Step 1 of 8 · Minute 0
You need a sheet of plain white paper, a pencil and three or more felt-tip markers in different colours. A ruler helps for the straight parts.
The hand looks flat.
Why
The arches are too low, or the lines too far apart.
Fix
Make the arches taller over the palm and draw the lines closer together, about 1 cm apart.
It looks lumpy.
Why
Arches of very different heights next to each other.
Fix
Change the height of the arches gradually from one line to the next, like the slope of a hill.
The fingers merge into a blob.
Why
The lines arch across the gaps between fingers.
Fix
Bring each line back down to straight in every gap between fingers, then arch again over the next finger.
04The illusion
Every line you draw is a straight path across the page, lifted wherever the hand would be in the way. Over the palm, which is wide and high, the lift is big and broad; over a finger, small and narrow. Your eye puts all the lifted lines together and sees a surface, the way it sees hills in a field of ploughed furrows.
Try it with a hand, a ball or a ripple, and change how much the lines lift:
Each line runs straight until it meets the hand, then arcs up over it and drops back down. Your brain reads the arcs as a surface curving towards you, the way a ribbon draped over a real hand would look. More lines and steadier colours make the effect stronger.
Each arch is really a slice through the hand, its outline along that line, tipped up to face you:
The orange line is the hand’s outline along that row, tipped up towards you. Look at a real hand from a low angle and a line across it would look just like this. From straight above, at 90°, there would be no bump at all; the lower the angle, the taller the bump looks, about 1.4 times the real height at 35°.
05The big idea
The brain
builds depth.
Your eyes only ever receive flat images. Depth is something your brain works out, from clues: shading, overlap, the way lines bend over surfaces. Give it the right clues and it builds a solid shape, even on paper.
Lifted lines are one of the strongest clues of all, which is why mapmakers, astronomers and engineers use them to show shapes, and why your drawn hand seems so convincingly real.
06The math
1 · The rule
y = y₀ − k · h(x, y₀)
Each line at height y₀ is lifted by the hand’s height h below it.
2 · Viewing angle
k = 1 ⁄ tan θ
Looking from θ above the table, heights appear multiplied by this.
3 · A finger
h = √(r² − d²)
A tube of radius r: the arch is a half-circle.
A finger about 2 cm wide is roughly a tube of radius 1 cm, so a line across it should rise in a half-circle about 1 cm high. Pretend you are looking from 35° above the table and k = 1 ⁄ tan 35° ≈ 1.4, so draw it 1.4 cm high. The palm is about 3 cm high in the middle, so its arches peak at about 4 cm.
Looking straight down, at 90°, k = 0: no lift, and the hand vanishes. Looking almost along the table, at 15°, k ≈ 3.7: towering arches. Somewhere between, about 30° to 45°, looks most natural.
07Real life
From mountain maps to album covers to road safety.
Contour maps
Maps show hills with contour lines, each joining points at the same height. In 1774, surveying the Scottish mountain Schiehallion to help weigh the Earth, the mathematician Charles Hutton drew some of the first contour lines on land.
Unknown Pleasures
The cover of Joy Division’s 1979 album is a stack of lifted lines: radio pulses from the first pulsar ever found, plotted one above another by the astronomer Harold Craft. It is the same trick as your hand, applied to starlight.
3D scanners
Many 3D scanners shine a pattern of straight stripes onto an object. A camera sees how the stripes bend over its surface and works out the shape, exactly reversing your drawing.
3D zebra crossings
In 2017 the Icelandic town of Ísafjörður painted a zebra crossing with shadows so that, to approaching drivers, its stripes seem to float above the road, encouraging them to slow down.
Op art
In the 1960s artists such as Bridget Riley painted canvases of nothing but lines and curves that seem to bulge, ripple and swell, using the same tricks of the eye your hand drawing does.
Light from above
Your brain assumes light comes from above. A shape shaded darker at the bottom looks like a bump; shaded at the top, a dent. That’s why a shadow on one side of your hand makes it pop up.
1979
In 1967 the astronomer Jocelyn Bell Burnell discovered the first pulsar, a spinning star that sends out a radio pulse every 1.3 seconds. A few years later Harold Craft, a graduate student, plotted a series of its pulses one above another, each line lifted where the signal was strong.
In 1979 that plot became the cover of Joy Division’s album Unknown Pleasures, one of the most famous images in music. It is drawn exactly like your hand: straight lines lifted by a hidden shape, so that a flat page shows a landscape.
08Is and isn’t
You need artistic talent to draw it.
Only straight lines and simple arches. The illusion comes from the method, not from skill at drawing hands.
The hand is drawn in perspective.
There is no vanishing point at all. Each line is just lifted by the height of the hand below it, a simple rule that the eye reads as depth.
It only works for hands.
It works for anything you can trace: a mug, a leaf, your initials, a toy. Rounded objects give the best effect.
Colour is just decoration.
A repeating colour order helps your eye follow each line across the hand, which makes the curved surface far easier to see.
09Go further
A
Your initials
Write your initials in big, fat bubble letters and fill them with lifted lines. Do they stand up off the page?
B
A hollow
Try arching the lines down instead of up over your hand. Does it now look like a hand-shaped hole in the paper?
C
Dark paper
Draw with white and coloured pencils on black paper. Does the effect look stronger or weaker?
D
A contour map
Draw lines round your hand instead, each a little inside the last, like a map of a hill. Which looks more 3D?
E
Squint test
Look at your finished drawing with one eye closed, then both. Which makes the hand look more solid, and why?
10Questions
Trace your hand lightly in pencil. With a marker, draw a straight line across the page up to the outline, arch it up over the hand, and carry on straight on the other side. Repeat every centimetre up the page, then fill the gaps with more coloured lines following the same curves. The hand seems to rise off the paper.
Each arch is what a straight line would look like if it were draped over a real hand and seen from a low angle. Your brain is used to reading curved lines on a surface as bumps and hollows, so a whole stack of them builds a convincing solid shape, even on flat paper.
Drawings made by lifting parallel lines over a shape are related to contour and ridgeline plots. Mapmakers use contour lines to show hills; scientists stack lines into ridgeline plots, like the famous plot of a pulsar on the cover of Joy Division’s album Unknown Pleasures.
Use more, closer lines and keep them evenly spaced. Make the arches taller over the palm and smaller over the fingers. Repeat the colours in a fixed order, and add a soft shadow along one edge of the outline, as if lit from the other side.
Anyone who can trace a hand and draw lines, roughly from age five upward. Younger children may need help keeping the arches smooth; older ones can try harder shapes, such as their initials or a face.
Safety · Completely safe. Use washable markers for younger artists, and put scrap paper underneath so the ink doesn’t mark the table.
All DIY cards →Keep wandering
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