Re: new public beta of Kalendis released

I see that the current K=166 calendar has it’s leap week years listed at http://individual.utoronto.ca/kalendis/leap/52-293_sym_leap_years.htm .

Here the years that are five years after previous are shown in bold type in either black or red. The black ones are 17 years after the previous bold face (so form the first year of a long row) and the red ones occur 11 years after the previous bold face (so form the first year of  a short row).

 

If this colouring were applied to K=146, it would not show up its symmetry. Instead once could boldface those leap years that occur six years before and after other leap years. These years occur in the middle of a long row in intervals of 17 or 28 years. A neat and symmetrical way of colouring rows would be to colour odd-numbered years red and even-numbered years black. Each block of successive leap years of one colour would correspond to a row.  

 

Here I show the first 293 years coloured thus:  003 009 015 020 026 031 037 043 048 054 060 065 071 077 082 088 093 099 105 110 116 122 127 133 139 144 150 155 161 167 172 178 184 189 195 201 206 212 217 223 229 234 240 246 251 257 263 268 274 279 285 291.

 You may see that the black bold type years occur once every 62 years within this cycle. The red bold type years occur once every 28 or 34 years alternately within the cycle.

Irv replies:  Thanks, Karl, for that suggestion, which I have now implemented in a revised public beta of Kalendis, and I have posted some updated leap year lists in that format.

A few things:

- I preferred to have the red color in the "minority", so red rows are the even-numbered years-within-cycle

- It was confusing not to always have the year-within-cycle displayed, so the report now always includes the first cycle at the epoch.

- With this formatting, "almost" symmetrical cycles having an even number of years per cycle (524, 400, 648, 62) look strikingly non-symmetrical because the color pattern takes a "flip" half-way through the cycle.

The leap year lists can be generated by the currently posted public beta of Kalendis, but here are links to a few that I have posted on-line:

Fully Symmetrical:

http://individual.utoronto.ca/kalendis/leap/52-293_sym_leap.htm

http://individual.utoronto.ca/kalendis/leap/69-389_sym_leap.htm

http://individual.utoronto.ca/kalendis/leap/58-327_sym_leap.htm

http://individual.utoronto.ca/kalendis/leap/30-169_sym_leap.htm

Almost Symmetrical:

http://individual.utoronto.ca/kalendis/leap/93-524_sym_leap.htm

http://individual.utoronto.ca/kalendis/leap/71-400_sym_leap.htm

http://individual.utoronto.ca/kalendis/leap/115-648_sym_leap.htm

http://individual.utoronto.ca/kalendis/leap/11-62_sym_leap.htm

The patterns are more obvious in the shorter cycles.