Is there a pattern in the times of sunrise and sunset during the year?

Yes. Depending on your location, the times of sunrise and sunset, and the length of the daylight period, varies in a sine-wave pattern. (Sine waves - see the link. Ignore the math; just look at the pictures.)

In the northern hemisphere, the winter solstice is on December 21 (plus or minus a day, depending on the cycle of leap years) and has the shortest day and longest night of the year. Each day after that, the sun rises a little earlier each morning and sets a little later each evening. For a few weeks, the differences are minuscule, but by mid-January you can see the days lengthening day by day.

At the spring equinox on March 21, the change-of-day-length is the fastest, and the day and night are of equal length. The days continue to get longer and longer, but at a slower and slower pace until early June. By then, it's difficult to see the days lengthening, but they do.

June 21 (plus or minus a day) is the summer solstice, the longest day of the year. After that, the days begin to get a little bit shorter each day, but at an accelerating pace. By September 21, the fall equinox, the day and night are equal again, and the day length is getting shorter each day at its fastest pace. The day-shortening begins to slow down, but the days continue to get shorter and shorter, until the winter equinox on December 21.

Then the cycle starts all over again. Lather, rinse, repeat. Reverse the dates in the Southern Hemisphere.

In tropical areas, there isn't all that much difference between summer and winter. At the equator, there isn't more than about 15 minutes variation in the time on sunrise or sunset all year long.

At high latitudes (in either direction), the day lengths get extreme; at the poles, the day and night are each 6 months long.

The U.S. Naval Observatory has a "Sunrise/Sunset Tables for One Year" at http://www.usno.navy.mil/USNO/astronomical-applications/data-services/rs-one-year; select your city (in the USA) or enter your latitude and longitude (anywhere) to get a one-year list for your location.