Tag: Sierpinski

theAbysmal Fractal Year

Through feats of mathemagic the days of the year make a series of Sierpiński triangles.

365 = 30 + 31 + 32 + 33 + 34 + 35 + 1

Taking this particular formula, the question becomes how to take a sequential progression of days to make of it some geometric structure. Adjusting the formula, we get:

365 = 1 + 31 + 32 + 33 + 34 + 35 + 1
= 363 + 2

theAbysmal 363-day calendar,provides a framework for this to sort itself out. The +2 days fall on Apr 5 and Sep 7. These last two dates fall 260 days from Dec 21 (the New Year Day of the 13-Month Calendar). As a result, Apr 5 has the same Number~Glyph as the coming in new year in 260 days, whereas Sep 7 has the same Number~Glyph as the previous new year 260 days ago. Apr 5 looks ahead to the future, Sep 7 looks back at the past.

The fractal image is presented here as 2-dimensional, but it creates a 3-D model of a fractal tetrahedron, with the final point occurring at Apr 5. This provides us a greater vantage to see further (farther?) into the future.

a series of six diminishing fractal triangles. At right, a sngle triangle pointed down. To its left, three triangles make a triangle with a hollow centre pointed up. to its left, a triangle made up of three of these hollow triangles pointed down. The next triangle is three of those pointed up, the next three pointed down and the largest pointed up. Each individual triangle is shaded a single colour, such that the overall effect from right to left is from green through blue and in the largest triangle, purple, red, orange, yellow, and green.
the 363-day Fractal Year

Each triangle represents one day. It’s shaded according to the prismatic year, where

Green = East & Spring
Yellow = South & Summer
Red = West & Autumn
Blue = North & Winter

Beginning at bottom left, progress up and down each trio of triangles to follow the day-to-day progress from Apr 6 all the way to Apr 5, the inverted triangle at right (Sep 7 is not included).

I imagine it as slowly but surely building a pyramid over the course of the year, to climb atop and get a better vantage of the distant future. The thing is, as each year passes, another one of these is completed, such that after three years, we have another level. After 9 years, yet another. 27, 81, 243 years all raise us to greater perspective.

Here’s the map of the dates:

a fractal triangle pointed upward. Each triangle that makes up the giant triangle has a date written in it in numeric month/day format. It begins at he bottom left on 4/6 and continues on a path up and down each triangle made of triangles. Two dates are blacked out: Sep 7 about halfway up on the right, and Apr 5 at the very top.
a map of theAbysmal fractal year, with gregorian dates in numeric month/day format. Begin at bottom left.