# Wolfram Mathematica

## The Cycle of Orthodox Easter Sundays

Using the new function FindRepeat, this example will show that the pattern of Orthodox Easter dates repeats every 532 years, and will also identify a simple way to discover that a new cycle has started.

For a given year, this function gives the {month, day} pair for the Orthodox Easter Sunday.

For example, Orthodox Easter in 2019 falls on Sunday, April 15, in the Julian calendar, which is Sunday, April 28, in the Gregorian calendar.

The date of Easter in Western Christianity is computed with a different algorithm and falls on April 21 for 2019. See this example of compiled computations for an analysis of Western Easter dates.

Compute all Orthodox Easter dates in the Julian calendar, from year 1 to year 10000.

The result can be any of the 35 days between March 22 and April 25.

The cycle of dates repeats every 532 years.

This is the distribution of possibilities for a single cycle, moving all dates to the same year, say 2000, for representation with DateHistogram.

Two consecutive years never have the same date for Easter.

March 22 appears four times in the cycle, so it cannot be used to mark the beginning of a cycle. However, on three occasions it will be followed by April 11 the next year, and on only one occasion it will be followed by April 10.

Then you can use the sequence March 22, April 10 to define a notion of the beginning of a new cycle. The function SequenceSplit will find those pairs, remove them and separate the 10000 days into sublists of length 530.