The eye-catching octagon, just inside the entrance of this venerable institution in Glasgow's Hillhead, was Gray's gift to the club after his two-year spell as its artist-in-residence came to an end.
And, fittingly for a club that has been serving the community for almost 140 years, the mural bears the legend, 'Refresh Mind, Refresh Body, Refresh Land and Refresh Love.'
The Western was in the news this week after Historic Scotland awarded its building, and that of its 'friendly rival', the Arlington Baths Club, A-listed status.
This means that both of these splendid Victorian edifices are now buildings of 'national or international significance'.
The Western's facade looks impressive enough from the outside, but it gives no indication as to the size of the actual building.
Inside, Fraser Makeham, the club's general manager, took me on a tour of the facilities.
It lasts quite a while - up and down flights of steps, in and out of the pool area, the gymnasium, the Turkish baths, the Russian baths, the saunas, the sports hall and the exercise room.It's the sort of place it is quite easy to get lost in.
Suspended over the pool are the trapeze, travelling rings and other gymnastic equipment, part of the traditional fixtures that have made the Western famous.
"We're now up to 2500 members and there's a waiting list for membership," Fraser says over a coffee in the Western's bar & bistro, The Deep End.
Some 85 per cent of them come from the West End - "which is an incredible figure ... we are very much a community venue for this part of Glasgow."
There are various entry fees and subscriptions: the junior members, of whom there are 600, pay annual subscriptions of between £100 and £150. The 'gentleman' member pays a one-off entry fee of £300 and an annual subscription of £600, payable in eight instalments. The oldest member is a man of 94.
In bygone years, when the Western was getting underway, its members included lots of people from the professions and other leading occupations: ship owners, professors, accountants, lawyers, bankers, manufacturers, publishers and physicians.
"The club prides itself on the traditions and ethos dating back to 1876," says Fraser. "We still look upon our members as gentlemen and ladies, and that is how the signage throughout the building refers to them.
"The primary functions are the baths, the Turkish baths, the hot rooms and the relaxation areas, though we expanded in 1995 with the opening of the W.M. Mann building, which gave us a gymnasium, the sports hall and the exercise studio."
Mr Mann, it should be mentioned at this point, is the Western's honorary secretary, and a key figure in the club's recent history.
"The Western took a different direction at that time, but it has paid dividends, not least because of the growth in membership," Fraser adds. "Then, we had 1300 members, so you can see how much we have grown since then."
There's no doubting the importance of the role played by Bill Mann, whose involvement goes back to the late 1970s.
"There were holes in the roof, the swimming pool, and the boilers weren't functioning," Fraser says, "and the membership levels were at an all-time low. But Bill, an entrepreneur, came in and took a lead role in changing the fortunes of the club.
"One of the first things he started was a development account within the club. Over time, it was built up to just over £700,000, and that money was used to finance the new part of the building in 1995.
"It's great that he is still here today, doing his bit as Honorary Secretary. He was instrumental in making sure we survived those tricky times back in the 1970s."
If it hadn't been for him, would the Western still be with us today? "It's very unlikely," Fraser acknowledges.
It's this ability to change, to anticipate new trends, that has kept the Western's head above water at a time when private and public gyms have become more popular.
The atmosphere - even on a quiet midweek lunchtime - is relaxed and unhurried. It really does seem like a private members' club that happens to have a pool and a gym attached.
As an added bonus, the 2500 members have free access up to twice a week to the Western Lawn Tennis & Squash Club in Hyndland and also to Hyndland Bowling Club.
But you don't have to be a member to get in here - recreational classes are open to non-members for between £4 and £7, depending on the class.
In the meantime, the A-list status has been warmly received here, as it has, a mile away, at the Arlington.
"It's a great accolade for us," Fraser says. "When Historic Scotland told us that the building was being A-listed, you can imagine the delight felt by the board and by the members."