A week is a long time in the arts. I took some days off, and while I was away, a long and winding story this newspaper has covered for years - the plan to build a major film studio on land at Straiton, outside Edinburgh - received a green light from the Government.

So it looks more likely now that the Pentland Studios will indeed be built, although with detailed planning permissions still to be sought, its the end of the beginning of that particular tale, rather than the beginning of the end. But apart from the building of that film studio complex - which could have a transformative impact on the film and TV industry in Scotland - the biggest new thing being built in Scotland's cultural world is a elegantly hulking mass on the banks of the Tay.

I was shown around the V&A Dundee, the new museum of design currently being constructed on the waterfront, and the £80m-budgeted building is coming on apace. At present, with a large but temporary coffer dam (12,000 tonnes of artificial land, essentially) between the museum and the river, it requires imagination to picture how the museum - which currently resemble two large, angular, slightly foreboding black ships in port - will relate to that famous river.

Much debated, especially when the project's price ballooned from £45m in 2015, both the force and some of the subtleties of the designs wrought by Japanese architect Kengo Kuma are becoming clearer. In particular the twisting, precipitous, three-storey walls, and the voids at their crest which will become windows and a balcony, are now beginning to be augmented by long, cast stone panels - which look like lengthy shelves, slats or beams. These 2,350 panels which almost entirely cover the dark hulks as they are now. Some are 4m long, and they weigh up to 3000kg (3 tonnes). The exterior is impressive - and viewing those looming dark cliffs, ones thoughts turn to science fiction - but it was the interiors which struck me the most. They are not fitted out at the moment (that will happen next year) but they are cavernous.

In particular, the areas where the bulk of the exhibitions will be staged, are capacious. The permanent galleries, the Scottish Design Galleries, are sizeable, and will eventually feature 250 objects, taken from 12,000 designated as Scottish by the V&A in London, as well as others such as the Charless Rennie Mackintosh Tea Room from Glasgow. But the temporary exhibition space is big: 1100 square metres, which makes it Scotland's largest museum-standard space for exhibitions, V&A Dundee say.

It will be these temporary exhibitions, many coming directly from South Kensington, which will, one imagines, be at the core of the museum's appeal to visitors, especially those visitors who will return time and again. V&A Dundee has set itself quite ambitious targets for its business plan - it wants to see 500,000 visits in its first year, 2018, and 350,000 a year after that.

This would put it in the top 70 attractions in the UK, going by the statistics compiled by the Association of Leading Visitor Attractions, above Stirling Castle, and if it rose above 500,000 it could challenge Edinburgh Zoo, which registered 574,175 visitors.

As Philip Long, its director, conceded, it is "fiercely hard to predict the popularity of anything". But he repeatedly stated his confidence in the attraction of this building, probably one of the most ambitious built cultural projects Scotland has seen for some time. It is turning into something remarkable.