In the universal language of simple forms, the circle (or the sphere) signifies both that which transcends man and remains beyond his reach (the sun, the cosmic totality, ‘God’), and also that which, at its own sub-lunar level, related to germinations, to the maternal, to the intimate. -Jacques Cauvin 
Where the (lava) surface is smoother, mysterious petroglyphs were carved… in this historic setting, the Kings' Course has been called a surreal golf experience. -Waikoloa Beach Resort .
One may say that we seek with our human hands to create a second nature in the natural world. -Cicero, 45 BCE
Wooler Golf Club extends along the gentle sloping north side of Dod Law, a hill dome a few miles south of the Scottish border in north Northumberland, England. Uphill from the golf links is the crest of Dod Law, the highest part of Doddington Moor . During the Neolithic, beginning about 6000 BP, was a time when marking stone with rock-art became a common expression in Northumberland. Fell sandstone outcrops in highland areas attracted hunters and the first herders. For photos: Dod Law album
Waikoloa Beach Resort’s two golf courses, near the South Kohala coast on Hawaii’s Big Island, surround the ‘Anaeho’omalu petroglyphs, now called the Waikoloa Petroglyph Reserve. Carving of petroglyphs began about 1000 BP on the horizontal and open pāhoehoe lava flows and was most intensive during the 14th to the 16th centuries. Bulldozing for the golf courses and artificial lakes in the 1970s-1980s eradicated at least half of the estimated 9000 petroglyphs encompassed within the original three-acre lava field.  For photos: ‘Anaeho’omalu/Waikoloa album
The two rock-art sites have in common a predominance of abstract markings almost all of which are cups, circles, and variations on circular elements, though spirals are absent from both sites. Both sites have "enclosure" designs, straight or curved grooves surronding other elements, usually cups. Yet it goes beyond motifs. Georgia Lee's observation, writing about Hawai’I Island, could easily apply as well to the rock-art of Northumberland. Indeed, it seems to me it is so clearly said it offers worthwhile insight when considering most sites:
It is place and place marking, more so than the petroglyphs themselves, that are of significance. Thus the petroglyphs gained significance in the association with place; and in the process of being marked, the significance of the places themselves heightened, inscribed with the powers that made then special in the first place. There is dialectic here, a re-enforcing rhythm that enables place to speak through symbol and symbol to speak through place. 
-  Cauvin, Jacques. 2000. The Birth of the Gods and the Origins of Agriculture. Cambridge: Cambridge University Press. p.132. Cited by Richard Bradley. 2012. In The Idea of Order: the Circular Archetype in Prehistoric Europe.
-  http://www.waikoloabeachgolf.com/kings-course
-  Dod Law, Main panel: http://rockartmob.ncl.ac.uk/main/d/
-  Lee, Georgia, and Edward Stasack. 1999. Spirit of place the petroglyphs of Hawaiʻi. pp.56-64.
-  Lee, Georgia. 2002. "Wahi Pana: Legendary places on Hawai ‘i Island." In Inscribed Landscapes: Marking and Making Place. pp 79-92. Edited by Bruno David and Meredith Wilson. University of Hawaiʻi Press.
Below: (1) Dod Law (Main Panel A) and (2) ‘Anaeho’omalu (Waikoloa Petroglyph Reserve.)