# Traits Documentation

NatDogs supply is 8064 as of block 830591. Frequency for each trait is a snapshot in time, and will change as new Bitcoin blocks containing the hex bits pattern "3b" are introduced.&#x20;

Every NatDog is unique, and all future NatDogs will be unique.&#x20;

## Special Traits

Special traits are traits that are **not found in every NatDog**. Nested and intersectional pattern sets are used to establish trait relationships and levels of rarity.\\

**Pattern Set "Contains 420"**\
Type: nested

| Function             | Trait                  | Frequency    |
| -------------------- | ---------------------- | ------------ |
| Contains “4” and "0" | Cigarette              | 1446 (17.9%) |
| Contains “420”       | + Dognip for cigarette | 38 (0.47%)   |

\
**Pattern Set "Contains 8s"**\
Type: nested

| Function             | Trait         | Frequency      |
| -------------------- | ------------- | -------------- |
| Contains "8" and "8" | Clock Right   | 977 (12.1%)    |
| Contains “88”        | + Bow Left    | 244 (3.0%)     |
| Contains “888”       | + Bitten Tail | 17 (0.2%)      |
| Contains “8888”      | + Alien Scar  | 1 (<0.1%)      |
| Contains “88888”     | + TBA         | 0 (unreleased) |

**Pattern Set "Contains 9s"**\
Type: nested

| Function             | Trait     | Frequency  |
| -------------------- | --------- | ---------- |
| Contains "9" and "9" | Bone      | 473 (5.9%) |
| Contains “99”        | Coin      | 244 (3.0%) |
| Contains “999”       | Shroom    | 17 (0.2%)  |
| Contains “9999”      | Alien Cat | 1 (<0.1%)  |

**Pattern Set "Contains 0s"**\
Type: nested

| Function         | Trait                 | Frequency      |
| ---------------- | --------------------- | -------------- |
| Contains “0”     | Earring Left          | 2572 (31.9%)   |
| Contains “00”    | + Earring Right       | 242 (3.0%)     |
| Contains “000”   | + Alien Earring Left  | 17 (0.2%)      |
| Contains “0000”  | + Alien Earring Right | 1 (<0.1%)      |
| Contains “00000” | + TBA                 | 0 (unreleased) |

**Pattern Set "Contains 1s"**\
Type: nested

| Function         | Trait        | Frequency      |
| ---------------- | ------------ | -------------- |
| Contains “11”    | Tennis Ball  | 152 (1.9%)     |
| Contains “111”   | + Alien Ball | 8 (0.1%)       |
| Contains “1111”  | + TBA        | 0 (unreleased) |
| Contains “11111” | + TBA        | 0 (unreleased) |

**Pattern Set "Contains perfect square"**\
Type: intersectional

<table><thead><tr><th width="209">Function</th><th width="169">Trait</th><th>Frequency</th></tr></thead><tbody><tr><td>Contains 4 digit perfect square AND core trait <em>eyes look right</em> is TRUE</td><td>Laser Eyes Right</td><td><p><br>207 (2.5%)</p><p></p></td></tr><tr><td>Contains 4 digit perfect square AND core trait <em>eyes look left</em> is TRUE</td><td>Laser Eyes Left</td><td>17 (0.2%)</td></tr><tr><td>Contains 4 digit perfect square AND core trait <em>eyes look crossed</em> is TRUE</td><td>Gold Fangs</td><td>2 (&#x3C;0.1%)</td></tr><tr><td>Contains 5 digit perfect square</td><td>Alien Dog</td><td>43 (0.5%)</td></tr><tr><td>Contains 6 digit perfect square</td><td>Shades</td><td>5 (&#x3C;0.1%)</td></tr></tbody></table>

\*Laser eyes has conditional variations based on "look direction" (see core traits). Laser eye direction will match the direction of look direction trait. \\

**Pattern Set "Is multiple"**\
Type: intersectional

| Function            | Trait           | Frequency  |
| ------------------- | --------------- | ---------- |
| Is multiple of “12” | Gold Collar     | 672 (8.3%) |
| Is multiple of “13” | Alien Tear      | 620 (7.7%) |
| Is multiple of “14” | Alien Collar    | 576 (7.1%) |
| Is multiple of “15” | Two Tone Choker | 536 (6.6%) |
| Is multiple of “16” | Firework        | 504 (6.3%) |
| Is multiple of “69” | Spikes Collar   | 116 (1.4%) |

**Pattern Set "Is multiple 11"**\
Type: intersectional

| Function             | Trait          | Frequency  |
| -------------------- | -------------- | ---------- |
| Is multiple of 11    | Tailsock       | 732 (9.1%) |
| Is multiple of “888” | Alien Tailsock | 8 (0.1%)   |

**Pattern "Power of 7"**\
Type: n/a (single trait)

| Function      | Trait              | Frequency    |
| ------------- | ------------------ | ------------ |
| Is power of 7 | Unconditional Love | 2509 (31.1%) |

**Pattern Set "Contains 6-digit Palindrome"**\
Type: n/a (single trait)

| Function                    | Trait     | Frequency |
| --------------------------- | --------- | --------- |
| Contains 6 digit palindrome | Alien Pup | 7 (<0.1%) |

**Pattern Set "Contains Fibonacci"**\
Type: intersectional

| Function                   | Trait         | Frequency      |
| -------------------------- | ------------- | -------------- |
| Contains 3 digit fibonacci | Blood drips   | 283 (3.5%)     |
| Contains 4 digit fibonacci | Brow Piercing | 4 (<0.1%)      |
| Contains 5 digit fibonacci | Halo          | 1 (<0.1%)      |
| Contains 6 digit fibonacci | TBA           | 0 (unreleased) |
| Contains 7 digit fibonacci | TBA           | 0 (unreleased) |

##

## Core Traits

Core traits are traits for which a variation is found in every **Natdog**. Exclusive pattern sets are used. \\

**Pattern Set "Side of Bitmap"**\
Type: Exclusive\
(establishes left/right/center segments of bitmap array assuming layout of 10000 districts per row).\\

| Function                                                    | Trait           | Frequency    |
| ----------------------------------------------------------- | --------------- | ------------ |
| <p>Last 4 digits are < 4800<br>(on left side of bitmap)</p> | Eyes look right | 6288 (78.0%) |
| <p>Last 4 digits are > 5200<br>(on left side of bitmap)</p> | Eyes look left  | 1424 (17.7%) |
| Last 4 digits > 4800 and < 5200 (center of bitmap)          | Eyes cross-eyed | 352 (4.4%)   |

**Digit-based Pattern sets**\
The following pattern sets assign traits based on the digits of Bitcoin block numbers. Digits are assigned in reverse order. So in the Bitcoin block number 456789, the numerical value for digit 1 is “9”. \
\
**Pattern set "Digit 1 value"**\
Type: exclusive\
Determines head color

<table><thead><tr><th width="195">Function</th><th width="295">Trait</th><th>Frequency</th></tr></thead><tbody><tr><td>D1 = 0</td><td>Head = Dark grey, shade 1</td><td>807 (10.0%)</td></tr><tr><td>D1 = 1</td><td>Head = Purple, shade 1</td><td>807 (10.0%)</td></tr><tr><td>D1 = 2</td><td>Head = Red, shade 1</td><td>804 (10.0%)</td></tr><tr><td>D1 = 3</td><td>Head = Yellow, shade 1</td><td>804 (10.0%)</td></tr><tr><td>D1 = 4</td><td>Head = Blue, shade 1</td><td>805 (10.0%)</td></tr><tr><td>D1 = 5</td><td>Head = Brown, shade 1</td><td>805 (10.0%)</td></tr><tr><td>D1 = 6</td><td>Head = Light grey, shade 1</td><td>808 (10.0%)</td></tr><tr><td>D1 = 7</td><td>Head = Green, shade 1</td><td>808 (10.0%)</td></tr><tr><td>D1 = 8</td><td>Head = Pink, shade 1</td><td>808 (10.0%)</td></tr><tr><td>D1 = 9</td><td>Head = Orange, shade 1</td><td>808 (10.0%)</td></tr></tbody></table>

\
**Pattern set "Digit 2 value"**\
Type: exclusive\
Determines body/tail color

<table><thead><tr><th width="195">Function</th><th width="292">Trait</th><th>Frequency</th></tr></thead><tbody><tr><td>D2 = 0</td><td>Body/Tail = Dark grey, shade 2</td><td>800 (9.9%)</td></tr><tr><td>D2 = 1</td><td>Body/Tail = Purple, shade 2</td><td>800 (9.9%)</td></tr><tr><td>D2 = 2</td><td>Body/Tail = Red, shade 2</td><td>800 (9.9%)</td></tr><tr><td>D2 = 3</td><td>Body/Tail = Yellow, shade 2</td><td>804 (10.0%)</td></tr><tr><td>D2 = 4</td><td>Body/Tail = Blue, shade 2</td><td>816 (10.1%)</td></tr><tr><td>D2 = 5</td><td>Body/Tail = Brown, shade 2</td><td>812 (10.1%)</td></tr><tr><td>D2 = 6</td><td>Body/Tail = Light grey, shade 2</td><td>800 (9.9%)</td></tr><tr><td>D2 = 7</td><td>Body/Tail = Green, shade 2</td><td>808 (10.0%)</td></tr><tr><td>D2 = 8</td><td>Body/Tail = Pink, shade 2</td><td>820 (10.2%)</td></tr><tr><td>D2 = 9</td><td>Body/Tail = Orange, shade 2</td><td>804 (10.0%)</td></tr></tbody></table>

\
**Pattern set "Digit 3 value"**\
Type: exclusive\
Determines left ear color

<table><thead><tr><th width="197">Function</th><th width="289">Trait</th><th>Frequency</th></tr></thead><tbody><tr><td>D3 = 0</td><td>Left ear = Dark grey, shade 2</td><td>800 (9.9%)</td></tr><tr><td>D3 = 1</td><td>Left ear = Purple, shade 2</td><td>800 (9.9%)</td></tr><tr><td>D3 = 2</td><td>Left ear = Red, shade 2</td><td>800 (9.9%)</td></tr><tr><td>D3 = 3</td><td>Left ear = Yellow, shade 2</td><td>816 (10.1%)</td></tr><tr><td>D3 = 4</td><td>Left ear = Blue, shade 2</td><td>800 (9.9%)</td></tr><tr><td>D3 = 5</td><td>Left ear = Brown, shade 2</td><td>816 (10.1%)</td></tr><tr><td>D3 = 6</td><td>Left ear = Light grey, shade 2</td><td>800 (9.9%)</td></tr><tr><td>D3 = 7</td><td>Left ear = Green, shade 2</td><td>800 (9.9%)</td></tr><tr><td>D3 = 8</td><td>Left ear = Pink, shade 2</td><td>800 (9.9%)</td></tr><tr><td>D3 = 9</td><td>Left ear = Orange, shade 2</td><td>832 (10.3%)</td></tr></tbody></table>

\
**Pattern set "Digit 4 value"**\
Type: exclusive\
Determines right ear color

<table><thead><tr><th width="197">Function</th><th width="268">Trait</th><th>Frequency</th></tr></thead><tbody><tr><td>D4 = 0</td><td>Right ear = Dark grey, shade 2</td><td>592 (7.3%)</td></tr><tr><td>D4 = 1</td><td>Right ear = Purple, shade 2</td><td>0 (unreleased)</td></tr><tr><td>D4 = 2</td><td>Right ear = Red, shade 2</td><td>744 (9.2%)</td></tr><tr><td>D4 = 3</td><td>Right ear = Yellow, shade 2</td><td>3000 (37.2%)</td></tr><tr><td>D4 = 4</td><td>Right ear = Blue, shade 2</td><td>2304 (28.6%)</td></tr><tr><td>D4 = 5</td><td>Right ear = Brown, shade 2</td><td>0 (unreleased)</td></tr><tr><td>D4 = 6</td><td>Right ear = Light grey, shade 2</td><td>0 (unreleased)</td></tr><tr><td>D4 = 7</td><td>Right ear = Green, shade 2</td><td>0 (unreleased)</td></tr><tr><td>D4 = 8</td><td>Right ear = Pink, shade 2</td><td>424 (5.3%)</td></tr><tr><td>D4 = 9</td><td>Right ear = Orange, shade 2</td><td>1000 (12.4%)</td></tr></tbody></table>

\
\
**Pattern set "Digit 5 value"**\
Type: exclusive\
Determines nose color

<table><thead><tr><th width="197">Function</th><th width="267">Trait</th><th>Frequency</th></tr></thead><tbody><tr><td>D5 = 0</td><td>Nose = Dark grey, shade 2</td><td>0 (unreleased)</td></tr><tr><td>D5 = 1</td><td>Nose = Purple, shade 2</td><td>0 (unreleased)</td></tr><tr><td>D5 = 2</td><td>Nose = Red, shade 2</td><td>5456 (67.7%)</td></tr><tr><td>D5 = 3</td><td>Nose = Yellow, shade 2</td><td>592 (7.3%)</td></tr><tr><td>D5 = 4</td><td>Nose = Blue, shade 2</td><td>2016 (25.0%)</td></tr><tr><td>D5 = 5</td><td>Nose = Brown, shade 2</td><td>0 (unreleased)</td></tr><tr><td>D5 = 6</td><td>Nose = Light grey, shade 2</td><td>0 (unreleased)</td></tr><tr><td>D5 = 7</td><td>Nose = Green, shade 2</td><td>0 (unreleased)</td></tr><tr><td>D5 = 8</td><td>Nose = Pink, shade 2</td><td>0 (unreleased)</td></tr><tr><td>D5 = 9</td><td>Nose = Orange, shade 2</td><td>0 (unreleased)</td></tr></tbody></table>

\
\
**Pattern set "Digit 6 value"**\
Type: exclusive\
Determines stripes color

<table><thead><tr><th width="197">Function</th><th width="289">Trait</th><th>Frequency</th></tr></thead><tbody><tr><td>D6 = 0</td><td>Stripes = Dark grey, shade 1</td><td>0 (unreleased)</td></tr><tr><td>D6 = 1</td><td>Stripes = Purple, shade 1</td><td>2016 (25.0%)</td></tr><tr><td>D6 = 2</td><td>Stripes = Red, shade 1</td><td>0 (unreleased)</td></tr><tr><td>D6 = 3</td><td>Stripes = Yellow, shade 1</td><td>0 (unreleased)</td></tr><tr><td>D6 = 4</td><td>Stripes = Blue, shade 1</td><td>0 (unreleased)</td></tr><tr><td>D6 = 5</td><td>Stripes = Brown, shade 1</td><td>0 (unreleased)</td></tr><tr><td>D6 = 6</td><td>Stripes = Light grey, shade 1</td><td>2016 (25.0%)</td></tr><tr><td>D6 = 7</td><td>Stripes = Green, shade 1</td><td>0 (unreleased)</td></tr><tr><td>D6 = 8</td><td>Stripes = Pink, shade 1</td><td>2016 (25.0%)</td></tr><tr><td>D6 = 9</td><td>Stripes = Orange, shade 1</td><td>0 (unreleased)</td></tr><tr><td>Null</td><td>Stripes = None</td><td>2016 (25.0%)</td></tr></tbody></table>
