# Traits Documentation

Natcats 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. 

Every Natcat is unique, and all future Natcats will be unique. 

## Special Traits

Special traits are traits that are **not found in every Natcat**. Nested and intersectional pattern sets are used to establish trait relationships and levels of rarity.<br>

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

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

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

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

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

| Function             | Trait            | Frequency  |
| -------------------- | ---------------- | ---------- |
| Contains "9" and "9" | Trout            | 473 (5.9%) |
| Contains “99”        | Salmon           | 244 (3.0%) |
| Contains “999”       | Alien Fish       | 17 (0.2%)  |
| Contains “9999”      | Giant Alien Fish | 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” | + Alien Tiara         | 0 (unreleased) |

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

| Function         | Trait                 | Frequency      |
| ---------------- | --------------------- | -------------- |
| Contains “11”    | Fly                   | 152 (1.9%)     |
| Contains “111”   | + Fly’s earring       | 8 (0.1%)       |
| Contains “1111”  | + Fly’s alien earring | 0 (unreleased) |
| Contains “11111” | + Fly’s laser eyes    | 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>Laser Eyes Crossed</td><td>2 (&#x3C;0.1%)</td></tr><tr><td>Contains 5 digit perfect square</td><td>Yarn</td><td>43 (0.5%)</td></tr><tr><td>Contains 6 digit perfect square</td><td>Laser Pointer</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. <br>

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

| Function            | Trait          | Frequency  |
| ------------------- | -------------- | ---------- |
| Is multiple of “12” | Rainbow Collar | 672 (8.3%) |
| Is multiple of “13” | Pearls         | 620 (7.7%) |
| Is multiple of “14” | Orange Collar  | 576 (7.1%) |
| Is multiple of “15” | Headband       | 536 (6.6%) |
| Is multiple of “16” | Sunhat         | 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    | Mouse       | 732 (9.1%) |
| Is multiple of “888” | Alien Mouse | 8 (0.1%)   |

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

| Function            | Trait       | Frequency    |
| ------------------- | ----------- | ------------ |
| Contains power of 7 | Nightvision | 2509 (31.1%) |

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

| Function                    | Trait         | Frequency |
| --------------------------- | ------------- | --------- |
| Contains 6 digit palindrome | Alien Diamond | 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 | Hammer        | 0 (unreleased) |
| Contains 7 digit fibonacci | Vial          | 0 (unreleased) |

##

## Core Traits

Core traits are traits for which a variation is found in every **Natcat**. Exclusive pattern sets are used. <br>

**Pattern Set "Side of Array"**\
Type: Exclusive\
(establishes left/right/center segments of an array assuming layout of 10000 block numbers per row, as a reference to metaverse frameworks like Bitmap).<br>

| Function                                                 | Trait           | Frequency    |
| -------------------------------------------------------- | --------------- | ------------ |
| <p>Last 4 digits are < 4800<br>(left side of array)</p>  | Eyes look right | 6288 (78.0%) |
| <p>Last 4 digits are > 5200<br>(right side of array)</p> | Eyes look left  | 1424 (17.7%) |
| Last 4 digits > 4800 and < 5200 (center of array)        | 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 = Indigo, shade 1</td><td>807 (10.0%)</td></tr><tr><td>D1 = 2</td><td>Head = Lilac, 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>

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**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 = Indigo, shade 2</td><td>800 (9.9%)</td></tr><tr><td>D2 = 2</td><td>Body/Tail = Lilac, 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 = Indigo, shade 2</td><td>800 (9.9%)</td></tr><tr><td>D3 = 2</td><td>Left ear = Lilac, 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 = Indigo, shade 2</td><td>0 (unreleased)</td></tr><tr><td>D4 = 2</td><td>Right ear = Lilac, 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 = Indigo, shade 2</td><td>0 (unreleased)</td></tr><tr><td>D5 = 2</td><td>Nose = Lilac, 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 = Indigo, shade 1</td><td>2016 (25.0%)</td></tr><tr><td>D6 = 2</td><td>Stripes = Lilac, 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>

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