Pkin Spiral Calendar
The Pkin Spiral Calendar (PSC) is a square spiral calendar used to depict a Practitioner's Pkin Cycle, which spans from the Practitioner's 12th birthday to their 24th. The Calendar consists of 12 Layers, plus a Core (which represents the End Point); each Layer is equal to 1 year, and each Quarter of said Layer is equal to 3 months. Each Layer contains a varying even number from 2-24/Quarter of vertical and horizontal line segments called Brackets.
Visually, time on the Calendar starts on the outer Layer from the top-left corner and moves clockwise around the spiral until it gets to the End Point; however, the day the Objective Pkin Calendar starts is March 1, with the end-date being February 28 or 29.
Figure 1: Diagram depicting the different parts of the Pkin Spiral Calendar. Click here to download the fill-in-the-blank version.
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NOTE: This depiction is slightly outdated; the names of certain parts (i.e "Cones" to "Triangles" and the update of the Leap Numbers from 1-4 to {0, +1, 2, -1}) have been changed since it was first drawn.
Bracket Duration Formula
The Bracket Duration Formula (BDF) is a mathematical formula used to figure out the time durations of the shortest horizontal and vertical line segments found in the continuum of the Pkin Spiral Calendar, according to Layer and Quarter. Please note that this does not include any of the line segments intersecting through the center of the Calendar (besides the one in the Left Quarter that connects to the Core) - just the ones on the spiral continuum.
Triangles
Because each month of the Gregorian Calendar varies in the amount of days, the amount in the term "3 months" will vary also. This results in each Quarter's amount of days being skewed to either 89, 90, 91 or 92. These are known as a Triangle Values - which, in turn, affect the calculation of the Bracket Durations depending on the Layer and Quarter a given Bracket is located on.
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Because of this, each Quarter (or Triangle) is given a single directional letter abbreviation to represent its general location on the Calendar:
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T = Top
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R = Right
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B = Bottom
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L = Left
What determines the specific time of year of these locations - and the amount of days ascribed to them - is whatever day a Personal PSC starts: the Practitioner's 12th birthday, which is depicted on the top-left corner.
Triangle Codes
A good starting place for determining the time of year for each Triangle is using the Practitioner's birth month, which will give us what is called their Triangle Code. A Triangle Code is the arrangement of the above abbreviations that expresses the order of each relevant Triangle Value from least to greatest; it also groups the Triangles with the highest amount of days together (since they always have an equal amount) and orders those chronologically. Each Triangle Value is separated by a dash, as shown below:
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If a Practitioner was born in March, their Triangle Code is L-B-TR
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If a Practitioner was born in April, their Triangle Code is L-T-RB
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If a Practitioner was born in May, their Triangle Code is L-TRB
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If a Practitioner was born in June, their Triangle Code is B-R-TL
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If a Practitioner was born in July, their Triangle Code is B-L-TR
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If a Practitioner was born in August, their Triangle Code is B-TRL
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If a Practitioner was born in September, their Triangle Code is R-T-BL
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If a Practitioner was born in October, their Triangle Code is R-B-TL
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If a Practitioner was born in November, their Triangle Code is R-TBL
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If a Practitioner was born in December, their Triangle Code is T-L-RB
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If a Practitioner was born in January, their Triangle Code is T-R-BL
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If a Practitioner was born in February, their Triangle Code is T-RBL
Figure 2: Chronological Table of Triangle Values, in days; you can use this to plug the different values of your Triangle Code into your own Calendar and do the math for each Layer from there.
Leap Numbers
Another thing that affects this are Pkin Leap Years (which, in Pkin Spiral Calendar terms, are called Leap Numbers), which tell you which Triangle and Layers of a Practitioner's personal PSC include Leap Day (February 29th), thereby making each Bracket on the affected Triangle and Layers slightly longer in than normal in terms of time. A Practitioner can have a Leap Number of either 0, +1, 2, or -1.
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If a Practitioner's Leap Number is 0, it means they were born during a Pkin Leap Year (March 1 - February 29). This also means the Layers including February 29th will be 1 (aka the Outer Shell), 5 and 9.
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If a Practitioner's Leap Number is +1, it means they were born the year after a Pkin Leap Year. This also means the Layers including February 29th will be 2, 6 and 10.
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If a Practitioner's Leap Number is 2, it means they were born roughly 2 years between two Pkin Leap Years. This also means the Layers including February 29th will be 3, 7 and 11.
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If a Practitioner's Leap Number is -1, it means they were born the year before a Pkin Leap Year. This also means the Layers including February 29th will be 4, 8 and 12.
Figure 3: Table depicting Pkin Cycle durations according to Leap Number.
Bracket Duration Calculator
Here's a handy calculator to use to figure out what your Calendar's bracket durations are:
Calculator Translations
In case you get confused about what the results from the above Calculator mean, here's a table of translations for various results in days, hours, minutes and seconds:
Figure 4: Table depicting division results of Bracket Duration Formula in Day/Hr/Min/Sec Format.