A South Korean number begins with the area code, 02 for Seoul and 03x to 06x for everywhere else, and there are only seventeen: one for each province and each of the metropolitan cities cut out of them. This map draws each code on its division, from the census boundaries, and the colour is the digit after the 0 — the region the plan laid the codes out by, from 3 around the capital to 6 in the south-west.
How to read the map. Each patch is a province or a metropolitan city and the numeral on it is its code, with the name beneath. Seoul alone has a two-digit code, 02; the rest are three, and the middle digit is the region: 3 is the capital's surroundings — Gyeonggi, Incheon and Gangwon — 4 Chungcheong with Daejeon and Sejong, 5 Gyeongsang with Busan, Daegu and Ulsan, 6 Jeolla with Gwangju, and Jeju. The metropolitan cities are enclaves in their old provinces and carry their own codes: Busan's 051 sits inside Gyeongnam's 055, Daegu's 053 inside Gyeongbuk's 054.
Where the lines come from. The plan of July 2000 gave every first-level division one code, replacing the hundred-odd codes of the cities and counties before it, and the only change since is Sejong, cut out of Chungnam in 2012 and given 044. So there is nothing to infer: the patches are Statistics Korea's division boundaries, and the code on each is the one the Ministry of Science and ICT assigns it. Ulleungdo and the islands of the west coast are drawn with their provinces; the islands too small to show at this scale dial the same codes.
Sources. Codes: Wikipedia, Telephone numbers in South Korea, for the seventeen area codes of the 2000 plan and their divisions. Geometry: Statistics Korea, census division boundaries, 2018, as published in southkorea/southkorea-maps under KOGL type 1; dissolved by region.