Complex Hex Book

A list of all the patterns I've discovered, as well as what they do.

Miscellaneous Complexes

UTF Purification (num/string → string/num)

Swaps between a string of a single character and an integer representing that character.
Uses the UTF-16 character map.

Bubbles

Bubbles' Purification (any → {any})

Pushes a Bubbled Iota, which when popped via execution (by Hermes' or the likes), will push the contained iota to the stack.

This is a collection of transcripts from a (now defunct) "Mathematics Corps". I'm not sure what use these have, but I would like to know what the researchers were on whilst writing them.

Complexities

Constant Imagination (→ complex)

Pushes 0 + 1i to the stack.

Constant Realisation (→ complex)

Pushes 1 + 0i to the stack.

Additive Distillation (complex, complex/num → complex)

Performs Addition, num will be treated as num + 0i.

Subtractive Distillation (complex, complex/num → complex)

Performs Subtraction, num will be treated as num + 0i.

Multiplicative Dstl. (complex, num → complex)

Performs Multiplication

Division Dstl. (complex, num → complex)

Performs Scalar Division.

Length Purification (complex → num)

Pushes the Argument (the length).

Power Distillation (num, complex → complex)

Performs Exponentiation.

Realising Complexities (complex → num)

Pushes the real coefficient.

Imagining Complexities (complex → num)

Pushes the imaginary coefficient.

Conjugation Prfn. (complex → complex)

Negates the imaginary coefficient of the topmost iota

Longs

Whilst normal numbers in the form of doubles are extremely useful in all sorts of cases, there come many times where they're just not precise enough.
To this end, longs are used. Despite their limitations (such as only storing integers, and a lower maximum value), longs are still useful due to this granularity, each bit of them can be manipulated freely without worry for imprecision.

Long Reflection (→ long)

Just like with normal numbers, Nature is not so generous as to make this easy for us.
(Details on next page)

Thankfully, what each angle does to the count is very similar to the norm, the only differences being:

a sharp left will shift the bits in the count to the left (effectively doubling them)

a sharp right will shift the bits in the count to the right (effectively halving them*)

* Due to a long's inability to contain a decimal, the value will always be rounded down.

Example: 43L

This pattern pushes 43L: (10 + 10 + 1) * 2 + 1 = 43

Long Purification (num/long → long/num)

Converts between doubles and longs
Always truncates the value when converting to long

Additive Distillation (long, long → long)

Perform Addition

Subtractive Distillation (long, long → long)

Perform Subtraction

Multiplicative Dstl. (long, long → long)

Perform Multiplication

Division Dstl. (long, long → long)

Perform Floored Division

Conjunction Distillation (long, long → long)

Perform Bitwise AND

Disjunction Distillation (long, long → long)

Perform Bitwise OR

Negation Purification (long, long → long)

Perform Bitwise NOT

Exclusion Distillation (long, long → long)

Perform Bitwise XOR

Left Shift Distillation (long, num → long)

Shifts all the bits to the left num times

Logical Right Shift Dstl. (long, num → long)

Shifts all the bits to the right num times

Arithmetic R. Shift Dstl. (long, num → long)

Shifts all the bits to the right num times while preserving the sign

Quaternionics

Quaternionic Exal. (num, vec → quaternion)

Pushes a Quaternion with num as the real coefficient and the vector's x, y, & z as the coefficients of i, j & k respectively.

Quaternionic Dntg. (quaternion → num, vec)

Pushes the real coefficient and a vector where the x, y, & z components are the coefficients of i, j, & k respectively.

Quaternionic Rfln.: 1 (→ quaternion)

Pushes 1 + 0i + 0j + 0k to the stack.

Quaternionic Rfln.: i (→ quaternion)

Pushes 0 + 1i + 0j + 0k to the stack.

Quaternionic Rfln: j (→ quaternion)

Pushes 0 + 0i + 1j + 0k to the stack.

Quaternionic Rfln: k (→ quaternion)

Pushes 0 + 0i + 0j + 1k to the stack.

Additive Distillation (qtrn, qtrn → quaternion)

Performs Addition

Subtractive Distillation (qrtn, qtrn → quaternion)

Performs Subtraction

Multiplicative Dstl. (quaternion, num → quaternion)

Performs Multiplication, Scalar if a num & quat are given, Hamiltonian if 2 quaternions are given.

Division Dstl. (quaternion, num → quaternion)

Performs Scalar Division.

Length Purification (quaternion → num)

Pushes the Argument (the length).

Quaterionic Prfn.: 1 (quaternion → num)

Pushes the coefficient of 1.

Quaterionic Prfn.: i (quaternion → num)

Pushes the coefficient of i.

Quaterionic Prfn.: j (quaternion → num)

Pushes the coefficient of j.

Quaterionic Prfn: k (quaternion → num)

Pushes the coefficient of k.

Quaternionic Inverse (quaternion → quat)

Negates the coefficients of i, j, & k

Matrixification (quaternion → matrix)

Pushes a matrix that (should) represent the same rotation as the quaternion

Quaterniation (matrix → quaternion)

Pushes a quaternion that (should) reperesent the same rotation as the matrix

Axis Angle Distillation (vec, num → quaternion)

Pushes a quaternion that reperesents a rotation by the given angle num radias around the given vector.

The spells catalogued here are purported to be of legendary difficulty and power. They seem to have been recorded only sparsely (for good reason, the texts claim). It's probably just the ramblings of extinct traditionalists, though -- a pattern's a pattern.

What could possibly go wrong?

BIT Manipulation

These are patterns to manipulate Block, Item, and Text Displays (BITs for short).

Oddly, Scout's Distillation does not seem to work on these, thus I must depend on Entity Prfn. or Zone Dstn.

Summon Block Display (vector, string →)

Summons a Block Display entity at the given position, displaying the given block. (The string must be the internal name i.e "minecraft:dirt", not "Dirt").
Costs about a Charged Amethyst

Summon Item Display (vector, string →)

Summons an Item Display entity at the given position, displaying the given item (The string must be the internal name i.e "minecraft:stick", not "Stick").
Costs about a Charged Amethyst

Summon Text Display (vector, string →)

Summons a Text Display entity at the given position, displaying the given string. Costs about a Charged Amethyst

Entity Purification: BIT (vector → entity)

Transform the position on the stack into the BIT at that location (or Null if there isn't one)

Zone Distillation: BIT (vector, number → [entity])

Take a position and a maximum distance on the stack, and combine them into a list of BIT's near the position.

Zone Distillation: Not BIT (vector, number → [entity])

Take a position and a maximum distance on the stack, and combine them into a list of non-BIT's near the position.

Translate BIT (BIT, vec →)

Translates the BIT to the given offset.

Rotate BIT (BIT, quat →)

Rotates the BIT to the given Quaternion.

Scale BIT (BIT, vec →)

Scales the BIT to the given vector.

Kill BIT (BIT →)

Kills & removes the given BIT.

This is the online version of the Complex Hex documentation.

Patterns