I've always been interested in maps, and even as a child I would take a map of the area south east of Peterborough and north of the A141 and draw, and quite well even if I say so, a map of a city I called Fenton. These days I'd need strong bifocals to produce what I did then.
Since then has come the Internet and a flowering of efforts to redraw the London Underground map as inherited from Harry Pick (I know - was it him and so on). With the addition of London Overground and the shifting Thameslink, and the coming of Crossrail, the map is hugely complicated. The more compromises it makes, the more the lines have to squiggle a bit, and the greater are some of its anomilies.
The principle of a good rapid transit map is as much simplicity as possible, and this means as many straight lines and regular curves as can be, and fewer deviations. One of the best and most recent adaptations of the London Rapid Transit map is by someone called Sameboat, who apparently resides in Hong Kong. The bottle shape of the original circle line, with the Metropolitan line above and the District line below he has tilted, which has allowed for improvements and corrections in other lines. There is still a bias to the centre and the lines outward are shrunken - he even flattens the outer lines into the horizontal.
However, originally, he did not include Thameslink or the Stansted Express, and Crossrail in the west involved a pretty horrendous compromise of the proposed Acton Main Line north of Action North, when it is most definitely to the south. Crossrail was nice and straight with few angles. However, when it came to later additions and adding in the new Thameslink, the line is forced into a curve downwards and then a sort of bucket shape before going towards the north west (heading for Milton Keynes). It is partly due to the tilted bottle, but also other line arrangements on the plan.
So I have had a go, especially as his effort was under a Creative Commons copyright. It's free for further development.
My effort is not just to include Crossrail and the new Thameslink, but putting back the old Thameslink (presumably the way to Moorgate goes via St Pancras now), and adding in the Stansted Express. My map is what I would like to see in terms of improved connectivity and a webpage gives complete explanations. For example, the Overground extension that passes over Brixton Underground Station has no station because it was too expensive to provide one. The new and coming (and expensive) link to Battersea (given in fact as a Northern Line extension: Sameboat oddly invents the Battersea line) has no intended connection to the Victoria Line because of expense and pressure on Vauxhall, when it goes under South Lambeth. This daft extension as is will force travellers to go the long way around Kennington and the Northern Line when the Victoria Line would have given a more direct route. There are other 'move and improve' changes like at Loughborough Junction and Harringay. On my map I have marked such changes for improved connectivity with yellow highlighting. Street maps show what is possible and not possible - Acton Junction adds to the large number of Acton stations both Underground and Overground, and why the Acton Main Line error had to be corrected (all it needs is for the Central Line to connect its two spurs with an alternative dominance of the upper northern branch over the lower southern). My map goes further south, to include the Wimbledon and Sutton loop that now forms part of Thameslink, and as a result improves the representation of the Tramlink, not only the sure necessity of an additional connecting to South Wimbledon by a spur but in how one long branch line turns in its dive towards South Croydon before going off south east. Sameboat showed a horizontal line for that. My 'improvements' as well as being larger were made by stretching the map north and slightly westwards beyond the bottle, thus in part countering the bottle's tilt. It's negative effect is on the Metropolitan line, but that was long and straight and station-avoiding anyway. It goes into the stretch zone, in effect.
Of course the bias on London means more than one Crossrail, I have not put more in. I have put in suggestions I think are the most rational and effective, trying to connect up the system and making the London Overground even more orbital - not just via Putney to and from Richmond, but via Twickenham as well.
I have used mainly the pre-ribbon MS Paint for my improvements, but did start to employ RealWorld Paint because of its facility with curves. I've done some smoothing via my old and trusty Micrografx Picture Publisher. I admire people like Sameboat, who can make .SVG files. How they do it baffles me.