Egglepple®

Creator+Composer: Link Starbureiy

Egglepple [pronunciation 'egg-ul-epp-ul'] is lnq's portfolio* (a finite succession [ie. walk] of convertible stews) and the subject of his repertoire.^{^} Generically, it is the polymorphic tape (itself a bugger puzzle) of leaf definitions (literally "egg leaf ↔ epp leaf"), and the formal name of our 26-dimensional membrane (SMALL∪BIG ⊂ Stewniverse) [as a stand-alone lyre (when controlled by the Stewdio) connecting both ends of The Origamic Symphony]. Specifically, it describes/refers to the kindergarten aspects.As in porting stews from one side of the leaf (recto) to the other side (verso). On the basis of quoting, risk tolerance increases with each proof and is infinite when completely solved (/totally sequenced). Egglepple is what gets juked. (not to be confused with The Egglepple Company, see also Egglepple, everywhere!, 📓Egglepple: Unfolded, 🎞️Egglepple: The Mathemagical World, yoyo, UUelcome, Quantumquotient, EGP, UUe, lnq's Starting Five, lnq's walk, Starbureiy nomenclature, mathemusic)

Notes (+): +Joey Koala is the official mascot of Egglepple. +Egglepple was invented and coined by Link Starbureiy.🤓 The word is also part of his name.😉 (see Starbureiy nomenclature)

Function map: preimage ← Egglepple → image ⇒ UUelcome

+mesh

A mesh is technically (mathematically-speaking) defined as a sheaf of branes that is outputted as an image. (see also meshroom, preimage)

+SMALL brane

As permutations of Egglepple, there are two (2) SMALL branes - a 0-brane and a 1-brane - comprising their own (lowest-level) class. (compare BIG brane)

Note (+): In terms of juking, the 0-brane is associated with some flageolet pencil.

+BIG brane

As permutations of Egglepple, there are twenty-four (24) BIG branes that comprise its/their own class - the 2-brane through 25-brane. Technically, these branes are any branes other than the SMALL branes [(0,1)-branes], and themselves are permutable.

+brane

A brane is some mathematical generalization of a category to one (1) or more higher dimensions.

My portfolio is a twenty-six dimensional (26-dim) toy [puzzleware] with braneworld structure according to pitch class:
0-brane = particle
1-brane = string
2-brane = membrane/sheet/tape
.
.
.
25-brane
(see also Egglepple, mesh)

+yoyo

lnq's yoyo is a spool of fibor acting as the simulacrum of Egglepple. It is used for dribbling [a ball traversing a 1-brane]*. In gameplay, the yoyo, krayon, and Stewdio^{^} comprise the primary mathemusical instrumentation in ballet performance [juking].A type of juggle in jukespace, where the yoyo appears as just plain/regular string (sans discs) readied for input [print staging] from the Stewdio. The Stewdio is the default mode, whereas the yoyo and krayon work in k-mode.

Note (+): For posterity, the yoyo (particularly the pullstring) is/was what eventually piqued my interest in string(theory + ludology).

+loopstring

The loopstring, or l-string, is a string of unstereotyped pencils. Technically, l-string is a sesquilinear random coiling* of a 1-brane (which is) concatenated to and from specified reading frames (egg and epp), and subject to certain conditions (such as being gameplay-compliant). The string may be open🔓 or closed🔒, but is closed by default (hence the term 'loop'). In fact, the main objective of each opus is to twist some variation of this object into a functionally unique fibor.As some measure of twistor space.

Notes (+): +In the context of the whole of string theory, the loopstring may colloquially be referred to as "toy string". We must be careful, however, to not confuse this "toy string" or its ludology (SL) with bosonic string theory (which is considered a "toy model" for which to introduce string theory education). +I named it "loopstring" from 'loopy quanta' plus 'superstring', even though both terms are misnomers.

An argument can be made that l-string is a rudimentary automaton. It is hypothesized that all games are (or any game can be) based on and around some primitive manifestation of this object. Hence, when we want to study the ludology of any phenomenon, we could start with a drawn l-string, and proceed from there.

+coverage

A coverage is the trigonometric posture (ie. formation) for surjectively graphing a [supersymmetric] zone on(to) some pitch.

As cryptographic shape schemes [puzzles], coverages are fundamentally mutable and dynamic; spanning the entire range of branes(SMALL + BIG). A coverage can be (strategically) both preventive and responsive. (see also #coverage, egg, epp, patchwork, cassette, Honne Bay)

+meshroom

To meshroom (v.) is to coordinate The Origamic Symphony within jukespace [TOS↦j]. It dictates that, because Egglepple is (ludologically) a p-brane* connecting the vector scale extrema, the notion of cell space algebras being conflated epimorphically within a curvilinear framework is important for defining variation (groove∪melody).In this case, 'p' stands for (my) 'portfolio'.😇

Meshrooming advances genetic algorithms [: fold measured (partite) monomers in order to deduce a mesh] for twistors by considering them as datapoints on a neural network (ie. flavor⇒sequence→mesh). (also of interest: loopstring, Pink program)

Note (+): Compositing is hypothesized to be accomplished under a single preimage.

Function map: j → pm [...eventual self-synthesis]

+string

A string (or 1-brane) is a one-dimensional (1d) curvilinear path integral (integrand) with (at most) two (2) endpoints (in/input and out/output) called nuts. Strings may be open🔓 or closed🔒, but not both. (see also brane, SMALL brane, loopstring, string ludology, thread, walk)

Computationally, a string is a stream (sequence) of preimages.

+pitch

The intonation field of a brane (particularly an l-string) is called its pitch, or the pitch. In practical terms, this is simply the dimension (ie. length) of some random coil as measured in stews [precisely, the measure between two (2) nuts]. (see also port, key, coverage)

Note (+): The pitch of the (subchem) yoke is Egglepple.

+key

A key is the pitch class of a brane. Keys define the chord progression of a walk (ie. nut movement). Each of the twenty-six (26) different keys (A-Z) is a complexity controller for Egglepple's points of measurement [framing]. (see also patch)

Big-O Tree™

Big-O Tree (BOT^!) is UUe's metre.Like 'algorithmic botany'.

Pursuant to symphonic compile time, BOT is our auction arguments map for measuring nuts [per brane (Egglepple) sequencing]. On this graph, each node represents a ballet and its spacetime complexity* [(P ⊆ E) ∝ T]. Thus, there are 676 (26²) parent branches on the tree🌴 stemming from said leaf ports.Cache flow

Notes (+): +The fitness workflow is the cumulative generation of loop-erased walks. +Although "Big-O" behaves mathematically like big O (limiting behavior of functions), the 'O' in the name is actually for 'org' (as in opus organization).

Issue-tracking and related specifications for Big-O Tree are indigenous to the UUelcome Matte. Such specifications help sew (control fibor threading) our cellular fabric. (see also bigo tree, Mathilda)
Function map: signature ↔ BOT ↔ pajamas

+walk

A walk is some playable* spacetime complex process (sequence of finite steps at fixed lengths). This is a plot of a nut's path (as it would traverse a brane, indicative of currency flow) with stochastic activity at specified movements (opening→middlegame→endgame). In all probability, walks chart a statistical distribution of their entropy (random variables transforming twistor space). Ludologically, some progression and its contrapuntal motion.
In proof theory, there are three (3) stages to a walk: (1) coil, (2) graphics, and (3) mesh.

We use walks as parse arguments in juking. (see also lnq's walk, sport, Pink program, route, tip, UUelcome)

Note (+): In automation, walks are approximate source directives.

Function map: preimage → walk → image

+epp

As c=2^(b-1)/2 {b∈ℤ→26, /max=25 (0-25) || b = brane count [which is of the sesquilinear form (e^-,e⁺)]}, an epp is the coverage's resultant as a half-integer spin statistic (negative parity[^-]).

The theory of epps is earl. stop leaf (see also egg, Egglepple)

Notes (+): +The formula is in direct correlation to spin-statistics. So, for example, when b is odd, say b=5, then c(=4) is an integer-spin (egg). When b is even, say b=8, then c(=11.3137085+) is a half-integer-spin (epp). The rational portion (floating point) of half-integer statistics contributes to seigniorage. Obviously, any negative value for b will yield an epp. (see juke tax) +Yes, there are twenty-six (26) integer values here; we denote "0" as (0-,0+) → having both negative(-) and positive(+) polarity in twistor space. For instance, -12 ... (0-,0+) ... +12 = [26]. The total number of coverages, c, is an upperbound for points on a curve, and so its number line must include 0 (hence 0 through 25). However, because any b=0 gives nonsensical values [error codes], the zeroes are discounted, and lower and upper bounds are just eleven (11). The minima (cover-0 = -11) is 0.015625 and the maxima (cover-25 = +11) is 32.

+egg

As c=2^(b-1)/2 {b∈ℤ→26, /max=25 (0-25) || b = brane count [which is of the sesquilinear form (e^-,e⁺)]}, an egg is the coverage's resultant as an integer spin statistic (positive parity[⁺]).

The theory of eggs is ellis. start leaf (see also epp, Egglepple)

Notes (+): +The formula is in direct correlation to spin-statistics. So, for example, when b is odd, say b=7, then c(=8) is an integer-spin (egg). When b is even, say b=4, then c(=2.82842712+) is a half-integer-spin (epp). The rational portion (floating point) of half-integer statistics contributes to seigniorage. Obviously, any negative value for b will yield an epp. (see juke tax) +Yes, there are twenty-six (26) integer values here; we denote "0" as (0-,0+) → having both negative(-) and positive(+) polarity in twistor space. For instance, -12 ... (0-,0+) ... +12 = [26]. The total number of coverages, c, is an upperbound for points on a curve, and so its number line must include 0 (hence 0 through 25). However, because any b=0 gives nonsensical values [error codes], the zeroes are discounted, and lower and upper bounds are just eleven (11). The minima (cover-0 = -11) is 0.015625 and the maxima (cover-25 = +11) is 32.

The Origamic Symphony™℗

Composer: Link Starbureiy
The Origamic Symphony (TOS) is a mathemusical simulacrum whose algorithmic composition lies generically between any 26-measure scale; but, architecturally, the Planck and nano scales [domains] (known as subchemistry, C_s). Specifically, it is the totality of Egglepple movements.

Resting atop the hypothesis that every brane arrangement is (geometrically) convertible, solvable, and scorable, TOS is responsive to the calculus of Egglepple resonances (the program of the portfolio imagined as frets pertinent to stereotyping EGP).

"There is this beautiful symphony playing - everywhere, all the time."^{^} - Link Starbureiy

The symphony treats the entire portfolio as a (single loopstring*) path integral (line) subject to integration (including integration-by-parts [the twisting of pencils]) and derivation. All walks are integrated in twistor space, and output some stew derivative.Symphonic evidence is its subject (Egglepple). A continuous function. (see also UUelcome, lnq's Starting Five)

Notes (+): +The Origamic Symphony is the score of UUelcome. +Here "origami" specifies "p-brane (membrane/frame) folding". Namely, it is the twisting of measures (length) between the Planck and nano scales.

+krayon

The krayon is a colloquy (for any number of) lnq's personal choice of flageolet pencil (conductional in jukespace).

Note (+): The spelling with a 'k' is of my recipe. It's actually (or would be) 'crayon🖍' (like the wax-based stylus), a favorite tool of mine used throughout my career for painting.

The krayon hosts a complete copy^@ of UUelcome, and is, defaultly, an artificially-styled membrane utensil covering lnq's yoyo finger, as his jointed digitus medius* [with an end serving as the ornamenter]. When called, it undocks/unwraps from the hand. lnq may (characteristically) also choose to wear the (dislodged) krayon held behind an ear.Coded only to me, the impresario. Any finger (usually aside from the pollex) should suffice. (see also yoyo, Stewdio, UUelcome Matte, Koala Krayon, lnq's bubblegum, cassette, k-mode)