Geometrical Spiral Calendaring System for Bitcoin
This article explores the pattern being displayed in bitcoin that links its cyclical behavior to a spiral representation of the number π. I have discovered a mathematical model that can be used as a calendaring system to forecast bitcoin cycle length.
YouTube video tutorial:
Introduction
Consider bitcoin cycles with start and end dates as defined on the picture and chart above. The spiral key is a representation of the number π in spiral format. Let a bitcoin cycle be an identifiable feature in the logarithmic chart of bitcoin’s USD exchange rate as illustrated via the color-coded segments.
Each cycle has a start and end degree position on the spiral key. The spiral key is broken into 10 sections, each 36°. Data for this analysis was gathered from the daily BTC/USD exchange rate provided by coinmetric.io.
The purpose of this model is to prove that it is possible to accurately forecast the start and end date of all bitcoin cycles using a simple mathematical formula. This formula has accurately forecasted and validated all bitcoin cycles since inception in 2010. Using this information, two mathematical theorem statements can be made.
Defining the Spiral Key: Full Cycles and their Position
The premise of the spiral key is that it can be used as a calendar. Positioning the Full Cycles on the calendar is critical to understanding the inputs needed for each formula.
On the spiral calendar, time starts at 0° when bitcoin first began trading in July of 2010. Each segment of the circumference of the spiral at a given radius equates to the days traveled during that cycle.
To date, five full cycles have completed, and we are in the middle of the 6th full cycle. The lime cycle begins at 0° and travels the circumference of the spiral at radius 1 until it ends at 108° when radius increases to 2. The orange cycle starts at 108° and travels the spiral at radius 2 and ends at 144° when radius increases to 3. The blue cycle begins at 144° and travels the spiral at radius 3 and ends at 288° when radius increases to 4. The brown cycle begins at 288° and travels the spiral at radius 4 and ends at 324° when radius increases to 5.
The fifth full cycle begins at 324° and travels the spiral at radius 5 until 504° when radius increases to 6. This full cycle encompasses the red, purple, and yellow cycles as these all occur at radius 5. These three cycles (red, purple, yellow) are mid-cycles, which are defined on the next page. The sixth full cycle is the cycle we are currently in. It travels from 504° to 828° along the spiral at radius 6. This cycle encompasses the turquoise, pink, and green mid-cycles, which all occur at radius 6.
Knowing Pi to 32 digits, when first 0 is encountered which ends the theorem, is crucial. The position of all future radius increases is known; thus, it is possible to position all bitcoin cycles, including future cycles, on the key.
On the BTC/USD price chart in logarithmic format, the five fully completed full cycles have all ended in unmistakable blow-off tops that form a very recognizable pattern in technical analysis which is a defining characteristic of a full cycle.
Defining the Spiral Key: Mid-Cycles and their Position
Once the spiral increases to radius 5 at 324°, Mid-Cycle events begin to occur. These mid-cycle events occur because the spiral aligns with a past radius increase from the prior full 360° revolution. Five such mid-cycles have occurred thus far; three at radius 5 and two at radius 6.
Beginning with radius 5, the first mid-cycle is the red cycle which runs from 324° to 360°, where it encounters the lime cycle starting position at 0° when radius increased to 1. The next cycle is the purple cycle that starts at 360° and ends at 468° where it encounters the radius increase of the orange cycle starting position at 108° when radius increased to 2. Finally, the yellow cycle runs from 468° to 504° which aligns with the start of the blue cycle at 144° when radius increased to 3. These cycles are defined as mid-cycle events as they all occur along the same radius on the spiral, in this case radius 5, where the spiral intersects a previous radius increase 360° prior. Mid-cycle events for radius 5 correspond to the red, purple, and yellow cycles. The yellow mid-cycle also marks the completion of the full cycle which traveled the circumference of the spiral from 324° to 504° in five 36° sections where the spiral increases again in radius.
Once the spiral increases to radius 6 at 504°, two more mid-cycle events occur along this radius. The first is the turquoise cycle, starting at 504° and ending at 648° which corresponds to the alignment of the radius increase at the start of the brown cycle at 288° when radius increased to 4. The next mid-cycle is the pink cycle which starts at 648° and ends at 684° which corresponds to the start of the red cycle at position 324° when radius increased to 5. The final cycle for radius 6, the green cycle, marks the end of the full cycle and does not align with a previous radius increase from the prior 360-degree revolution.
Mid-cycle events mark either a new local low or a new all-time high in the BTC/USD exchange rate. Two mid-cycle events that mark a new local low (red, pink) have occurred 36°, or one section, from a previous cycle that ended in a new all-time high. One (yellow), did not, but coincided at the same degree as a full cycle end.
Using this information, the mathematical proofs for each cycle are presented below.
Theorem Statement Proofs
Each statement’s proof is provided in this section, starting with the first cycle, the lime cycle. The proofs are presented in chronological order with accompanying charts and calculations for each cycle. The difference between theorem and actual cycle length is provided in absolute value for comparison.
Lime Cycle Calculation
Orange Cycle Calculation
Blue Cycle Calculation
Brown Cycle Calculation
Red Cycle Calculation
Purple Cycle Calculation
A supplementary theorem statement #2 proof for the purple cycle can be obtained using the prior brown full cycle as input to calculate the entire length of the full cycle comprising red + purple + yellow. The entire full cycle at radius 5 travels five 36-degree sections on the spiral. The purple cycle is three of those five 36-degree sections. Therefore, calculating the entire duration of the red + purple + yellow cycle using the brown cycle as input and multiplying by 3/5 can also be used as a proof.
Yellow Cycle Calculation
The yellow cycle also marks the completion of the full cycle at radius 5, traveling the circumference of the spiral from 324° to 504° in five 36° sections. A supplementary theorem statement #2 proof for the full cycle calculation is detailed below.
Turquoise Cycle Calculation
A supplementary theorem statement #2 proof for the turquoise cycle can also be used to determine cycle length. Combining red, purple, and yellow mid-cycles into a single full cycle for use as input into the formula also proves the theorem for the turquoise cycle. The red, purple, and yellow cycles all travel the circumference of the spiral at radius 5 over the course of five 36° sections from 324° to 504°.
Pink Cycle Calculation
A supplementary theorem statement #2 proof for the pink cycle can be obtained using the prior full cycle at radius 5 as input to calculate the entire length of the full cycle at radius 6 comprising turquoise, pink, and green. The entire full cycle at radius 6 travels nine 36-degree sections on the spiral. The pink cycle is one of those nine 36-degree sections. Therefore, calculating the entire duration of the full cycle at radius 6 and multiplying by 1/9 can also be used as a proof.
Green Cycle Calculation
The chart below is an estimate of the entire length of the Pump Cycle Theorem. It has the potential to continue until the first zero in Pi is encountered after the 32nd cycle. Only full cycles are listed here and statement #2 is used to calculate the duration in the Theorem column.
Theorem Tolerance
The tolerance of each cycle is defined as the difference between actual and theorem, divided by the overall cycle length. Each cycle’s tolerance values are listed below in chronological order. This can be thought of as the margin of error for each calculation.
The very first two cycles suffer from very short cycle length which impacted their results. As cycles lengthen over time the tolerance decreases significantly. Alternatively, the absolute value of the difference between actual cycle length and theorem is a better measure of accuracy, as longer cycles could potentially mask a wider difference as an acceptable margin of error percentage when using this type of calculation. The widest difference in theorem versus actual to-date is the statement #1 proof of the blue cycle, which is 46 days. The narrowest difference to-date is the statement #1 proof of the orange cycle, at 4.2 days. All other cycles fall within this range for both statement #1 and statement #2 proofs.
Conclusion
The Pump Cycle Theorem chains all BTC/USD price cycles together into a single formula that can be used as a calendaring system to delineate bitcoin cycles. The model has been able to forecast and validate every bitcoin cycle since inception in 2010. The premise of the model is to forecast and validate the dates of new all-time highs and new local lows to within an acceptable tolerance. The difference between model and actual must stay within an acceptable tolerance for the theorem to keep its validity, which since 2013 has been a 1% to 4% margin of error.
The total potential of the theorem is 32 cycles, ending when the first zero in Pi is encountered. Whether or not all 32 cycles play out is unclear, but if so, it runs until approximately the year 2441. The spiral key can be seen in a crop circle formation found at Barbury Castle in Wiltshire, UK in June of 2008. Coincidently, this formation occurred just before bitcoin was set in motion a few months later. Could the genesis block in the bitcoin blockchain, referencing a UK bank, have been a hint telling everyone where to look to find the secret geometric pattern? A pattern which reveals a unique geometric calendaring system that allows forecasting of the future as well as validation of the past.
REFERENCES
1. Spiral Pi art, rounded up to 10 digits — https://www.lastofdays.co.za/cropcircles/crop_circles.htm
2. CSV chart data — https://charts.coinmetrics.io/crypto-data
