These are some other ways of looking at the calendar that I've seen over the years. Most of them are just offsets from a specific date in the past, the lunar phase tracker is the only one that uses the normal Gregorian calendar.
Human Era
Used by the folks at Kurzgesagt, this calendar is based on the rough estimate of the beginnings of agriculture, and thus the first big step toward civilization. By happy coincidence this is roughly 10,000 BCE on the Gregorian calendar so the Human Era year is the current year plus ten thousand.
Any calendar that tracks the solar year, like the Chinese calendar, or (on average, over time) the Hebrew calendar, will have an offset of something other than 10,000, which makes it tougher to remember if that's the only calendar you use. But most countries have settled on the Gregorian calendar, at least for civil life, so the +10,000 scheme should work for most people.
The Muslim calendar treats 12 lunar months as a year -- which is why Ramadan moves backward in the Gregorian calendar every year -- and would currently (early 2023) have a correction factor of 10,967 that will increment to 10,968 soon, and change again every 32 or 33 years.
Current date:
Eternal September
This goes back to the Usenet days, when there would be a burst of newcomers every September as people arrived at college, got their first-ever internet connection, and proceeded to be a pain in all the old-timers' asses until they figured out each group's vibe. Then in late 1993 AOL connected to Usenet and it all went to hell. And stayed there.
Current date:
Covid Calendar
Remember March 2020? When if we all stayed inside for a few weeks the virus would run its course? Somehow we're still there.
Current date:
Lunar Phases
The closest of these to actual programming, versus just doing some addition or subtraction. Shows the upcoming phase of the moon, based on a sydonic lunar cycle of 29.5306 days and assuming each phase is ¼ of that. The starting point I picked is the full moon of 23:09:55 UTC on January 6, 2023 (the upcoming full moon as I write this).
Upcoming phase:
