I want to use the following diagram on the cover image of a textbook:
- What aspects should I change to make it more suitable for this purpose?
- How can I make it look more modern? Should I add some colors?
I think that the diagram conveys a solemn style, which most probably fits the the content of your book and would be destroyed by many conceivable “modernisations”. As a normal textbook illustration, it is almost perfect, and you should keep the aspect that make it such on the cover. The most important quality of a math textbook is the intelligibility of the content and this is something your cover should convey – rather than being “fancy”. In particular I would advise against:
That being said, there is one main aspect I would change for the cover and this is the composition of elements. While it is alright within the textbook where the diagram should not occupy too much space (not only for economic reasons but also because you want to avoid the reader having to turn pages more than necessary) and is surrounded by text, on the cover you usually have a roughly quadratic space available, which you should use. In detail:
As for colour, I would suggest only to use two or three colours and only to distinguish certain types of elements. For example you could colour the arrows for the mappings and the corresponding legend differently from the rest and leave it at that. I would not use a different colour for the grids, as it would put too much emphasis on them.
Some further remarks:
The arrowheads are very prominent. I would rather use non-solid arrowheads instead, e.g., like this:
¹ This may be an effect of the low-resolution rendering, though. Confirm this before continuing.