Slide 1

The Roget Illusion and the
Persistence of Vision
by
J. L. Hunt
Dept. of Physics
Univ. of Guelph

Peter Mark Roget
(1779-1869)
the author of the famous Thesarus
noticed an unusual illusion

When a carriage wheel rolls behind
A picket fence (palisade) it does
NOT look like this

It looks like……..

THIS!!!

Which is known as

The Roget (Palisade) Illusion

A simple apparatus demonstrates
the illusion. An endless palisade
Is turned by a crank and a fixed
wheel rolls behind it.

Here’s what you see looking at the rolling
wheel through the palisade

Let’s follow the
intersection
of a spoke and
a slit as the wheel
rotates and the
array of slits
moves across.

Roget Illusion
Special case
N = 16, f = 0
1

This is one of the few illusions that can be
analyzed mathematically. The x and y
coordinates of the spoke and slit intersection
are:
x = rt
y = x tan [2n /N + x/r]
Where
r = radius of the wheel
 = angular velocity of the wheel
N = number of spokes in the wheel
n = 0……(N-1) is an index of a particular spoke.

y

0.5

0

-0.5

-1
0

0.5
x

1


Slide 2

The Roget Illusion and the
Persistence of Vision
by
J. L. Hunt
Dept. of Physics
Univ. of Guelph

Peter Mark Roget
(1779-1869)
the author of the famous Thesarus
noticed an unusual illusion

When a carriage wheel rolls behind
A picket fence (palisade) it does
NOT look like this

It looks like……..

THIS!!!

Which is known as

The Roget (Palisade) Illusion

A simple apparatus demonstrates
the illusion. An endless palisade
Is turned by a crank and a fixed
wheel rolls behind it.

Here’s what you see looking at the rolling
wheel through the palisade

Let’s follow the
intersection
of a spoke and
a slit as the wheel
rotates and the
array of slits
moves across.

Roget Illusion
Special case
N = 16, f = 0
1

This is one of the few illusions that can be
analyzed mathematically. The x and y
coordinates of the spoke and slit intersection
are:
x = rt
y = x tan [2n /N + x/r]
Where
r = radius of the wheel
 = angular velocity of the wheel
N = number of spokes in the wheel
n = 0……(N-1) is an index of a particular spoke.

y

0.5

0

-0.5

-1
0

0.5
x

1


Slide 3

The Roget Illusion and the
Persistence of Vision
by
J. L. Hunt
Dept. of Physics
Univ. of Guelph

Peter Mark Roget
(1779-1869)
the author of the famous Thesarus
noticed an unusual illusion

When a carriage wheel rolls behind
A picket fence (palisade) it does
NOT look like this

It looks like……..

THIS!!!

Which is known as

The Roget (Palisade) Illusion

A simple apparatus demonstrates
the illusion. An endless palisade
Is turned by a crank and a fixed
wheel rolls behind it.

Here’s what you see looking at the rolling
wheel through the palisade

Let’s follow the
intersection
of a spoke and
a slit as the wheel
rotates and the
array of slits
moves across.

Roget Illusion
Special case
N = 16, f = 0
1

This is one of the few illusions that can be
analyzed mathematically. The x and y
coordinates of the spoke and slit intersection
are:
x = rt
y = x tan [2n /N + x/r]
Where
r = radius of the wheel
 = angular velocity of the wheel
N = number of spokes in the wheel
n = 0……(N-1) is an index of a particular spoke.

y

0.5

0

-0.5

-1
0

0.5
x

1


Slide 4

The Roget Illusion and the
Persistence of Vision
by
J. L. Hunt
Dept. of Physics
Univ. of Guelph

Peter Mark Roget
(1779-1869)
the author of the famous Thesarus
noticed an unusual illusion

When a carriage wheel rolls behind
A picket fence (palisade) it does
NOT look like this

It looks like……..

THIS!!!

Which is known as

The Roget (Palisade) Illusion

A simple apparatus demonstrates
the illusion. An endless palisade
Is turned by a crank and a fixed
wheel rolls behind it.

Here’s what you see looking at the rolling
wheel through the palisade

Let’s follow the
intersection
of a spoke and
a slit as the wheel
rotates and the
array of slits
moves across.

Roget Illusion
Special case
N = 16, f = 0
1

This is one of the few illusions that can be
analyzed mathematically. The x and y
coordinates of the spoke and slit intersection
are:
x = rt
y = x tan [2n /N + x/r]
Where
r = radius of the wheel
 = angular velocity of the wheel
N = number of spokes in the wheel
n = 0……(N-1) is an index of a particular spoke.

y

0.5

0

-0.5

-1
0

0.5
x

1


Slide 5

The Roget Illusion and the
Persistence of Vision
by
J. L. Hunt
Dept. of Physics
Univ. of Guelph

Peter Mark Roget
(1779-1869)
the author of the famous Thesarus
noticed an unusual illusion

When a carriage wheel rolls behind
A picket fence (palisade) it does
NOT look like this

It looks like……..

THIS!!!

Which is known as

The Roget (Palisade) Illusion

A simple apparatus demonstrates
the illusion. An endless palisade
Is turned by a crank and a fixed
wheel rolls behind it.

Here’s what you see looking at the rolling
wheel through the palisade

Let’s follow the
intersection
of a spoke and
a slit as the wheel
rotates and the
array of slits
moves across.

Roget Illusion
Special case
N = 16, f = 0
1

This is one of the few illusions that can be
analyzed mathematically. The x and y
coordinates of the spoke and slit intersection
are:
x = rt
y = x tan [2n /N + x/r]
Where
r = radius of the wheel
 = angular velocity of the wheel
N = number of spokes in the wheel
n = 0……(N-1) is an index of a particular spoke.

y

0.5

0

-0.5

-1
0

0.5
x

1


Slide 6

The Roget Illusion and the
Persistence of Vision
by
J. L. Hunt
Dept. of Physics
Univ. of Guelph

Peter Mark Roget
(1779-1869)
the author of the famous Thesarus
noticed an unusual illusion

When a carriage wheel rolls behind
A picket fence (palisade) it does
NOT look like this

It looks like……..

THIS!!!

Which is known as

The Roget (Palisade) Illusion

A simple apparatus demonstrates
the illusion. An endless palisade
Is turned by a crank and a fixed
wheel rolls behind it.

Here’s what you see looking at the rolling
wheel through the palisade

Let’s follow the
intersection
of a spoke and
a slit as the wheel
rotates and the
array of slits
moves across.

Roget Illusion
Special case
N = 16, f = 0
1

This is one of the few illusions that can be
analyzed mathematically. The x and y
coordinates of the spoke and slit intersection
are:
x = rt
y = x tan [2n /N + x/r]
Where
r = radius of the wheel
 = angular velocity of the wheel
N = number of spokes in the wheel
n = 0……(N-1) is an index of a particular spoke.

y

0.5

0

-0.5

-1
0

0.5
x

1


Slide 7

The Roget Illusion and the
Persistence of Vision
by
J. L. Hunt
Dept. of Physics
Univ. of Guelph

Peter Mark Roget
(1779-1869)
the author of the famous Thesarus
noticed an unusual illusion

When a carriage wheel rolls behind
A picket fence (palisade) it does
NOT look like this

It looks like……..

THIS!!!

Which is known as

The Roget (Palisade) Illusion

A simple apparatus demonstrates
the illusion. An endless palisade
Is turned by a crank and a fixed
wheel rolls behind it.

Here’s what you see looking at the rolling
wheel through the palisade

Let’s follow the
intersection
of a spoke and
a slit as the wheel
rotates and the
array of slits
moves across.

Roget Illusion
Special case
N = 16, f = 0
1

This is one of the few illusions that can be
analyzed mathematically. The x and y
coordinates of the spoke and slit intersection
are:
x = rt
y = x tan [2n /N + x/r]
Where
r = radius of the wheel
 = angular velocity of the wheel
N = number of spokes in the wheel
n = 0……(N-1) is an index of a particular spoke.

y

0.5

0

-0.5

-1
0

0.5
x

1


Slide 8

The Roget Illusion and the
Persistence of Vision
by
J. L. Hunt
Dept. of Physics
Univ. of Guelph

Peter Mark Roget
(1779-1869)
the author of the famous Thesarus
noticed an unusual illusion

When a carriage wheel rolls behind
A picket fence (palisade) it does
NOT look like this

It looks like……..

THIS!!!

Which is known as

The Roget (Palisade) Illusion

A simple apparatus demonstrates
the illusion. An endless palisade
Is turned by a crank and a fixed
wheel rolls behind it.

Here’s what you see looking at the rolling
wheel through the palisade

Let’s follow the
intersection
of a spoke and
a slit as the wheel
rotates and the
array of slits
moves across.

Roget Illusion
Special case
N = 16, f = 0
1

This is one of the few illusions that can be
analyzed mathematically. The x and y
coordinates of the spoke and slit intersection
are:
x = rt
y = x tan [2n /N + x/r]
Where
r = radius of the wheel
 = angular velocity of the wheel
N = number of spokes in the wheel
n = 0……(N-1) is an index of a particular spoke.

y

0.5

0

-0.5

-1
0

0.5
x

1


Slide 9

The Roget Illusion and the
Persistence of Vision
by
J. L. Hunt
Dept. of Physics
Univ. of Guelph

Peter Mark Roget
(1779-1869)
the author of the famous Thesarus
noticed an unusual illusion

When a carriage wheel rolls behind
A picket fence (palisade) it does
NOT look like this

It looks like……..

THIS!!!

Which is known as

The Roget (Palisade) Illusion

A simple apparatus demonstrates
the illusion. An endless palisade
Is turned by a crank and a fixed
wheel rolls behind it.

Here’s what you see looking at the rolling
wheel through the palisade

Let’s follow the
intersection
of a spoke and
a slit as the wheel
rotates and the
array of slits
moves across.

Roget Illusion
Special case
N = 16, f = 0
1

This is one of the few illusions that can be
analyzed mathematically. The x and y
coordinates of the spoke and slit intersection
are:
x = rt
y = x tan [2n /N + x/r]
Where
r = radius of the wheel
 = angular velocity of the wheel
N = number of spokes in the wheel
n = 0……(N-1) is an index of a particular spoke.

y

0.5

0

-0.5

-1
0

0.5
x

1


Slide 10

The Roget Illusion and the
Persistence of Vision
by
J. L. Hunt
Dept. of Physics
Univ. of Guelph

Peter Mark Roget
(1779-1869)
the author of the famous Thesarus
noticed an unusual illusion

When a carriage wheel rolls behind
A picket fence (palisade) it does
NOT look like this

It looks like……..

THIS!!!

Which is known as

The Roget (Palisade) Illusion

A simple apparatus demonstrates
the illusion. An endless palisade
Is turned by a crank and a fixed
wheel rolls behind it.

Here’s what you see looking at the rolling
wheel through the palisade

Let’s follow the
intersection
of a spoke and
a slit as the wheel
rotates and the
array of slits
moves across.

Roget Illusion
Special case
N = 16, f = 0
1

This is one of the few illusions that can be
analyzed mathematically. The x and y
coordinates of the spoke and slit intersection
are:
x = rt
y = x tan [2n /N + x/r]
Where
r = radius of the wheel
 = angular velocity of the wheel
N = number of spokes in the wheel
n = 0……(N-1) is an index of a particular spoke.

y

0.5

0

-0.5

-1
0

0.5
x

1