Stripe enumeration of ℕ × ℕ

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The stripe enumeration of

ℕ  ×  ℕ

is a bijection (one-to-one and onto mapping) from

ℕ

to

ℕ  ×  ℕ

, where

ℕ = {0, 1, 2, ...}

.

Pairing function

(...)

ℕ → ℕ  ×  ℕ

(...)

ℕ  ×  ℕ → ℕ

(...)

A319571 The stripe enumeration of

ℕ  ×  ℕ

where

ℕ = {0, 1, 2, ...}

, also called boustrophedonic Cantor enumeration. Terms are interleaved

x

and

y

coordinates.

{0, 0, 0, 1, 1, 0, 2, 0, 1, 1, 0, 2, 0, 3, 1, 2, 2, 1, 3, 0, 4, 0, 3, 1, 2, 2, 1, 3, 0, 4, 0, 5, 1, 4, 2, 3, 3, 2, 4, 1, 5, 0, 6, 0, 5, 1, 4, 2, 3, 3, 2, 4, 1, 5, 0, 6, 0, 7, 1, 6, 2, 5, 3, 4, 4, 3, 5, 2, 6, 1, 7, 0, 8, 0, 7, 1, 6, 2, 5, 3, 4, 4, 3, 5, 2, 6, 1, ...}

A319572 The

x

coordinates of the stripe enumeration of

ℕ  ×  ℕ

where

ℕ = {0, 1, 2, ...}

.

{0, 0, 1, 2, 1, 0, 0, 1, 2, 3, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 11, 10, 9, 8, 7, 6, ...}

A319573 The

y

coordinates of the stripe enumeration of

ℕ  ×  ℕ

where

ℕ = {0, 1, 2, ...}

.

{0, 1, 0, 0, 1, 2, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, ...}

Stripe enumeration path

Stripe enumeration path expressed with absolute headings

(...)

Stripe enumeration path expressed with relative headings

(...)

See also

• Shell enumeration of ℕ × ℕ