Looking for project ideas to match my interests
I am a former physician, having done half graduation in mechanical engineering, then a master degree in product design. Nowadays, I work for a biomedical/bioelectric-equipment company, doing mostly software design (algorithms and workflow), using Numpy (matlab like) for prototyping.

THAT fulfills my need (incredibly similar to yours) to solve new problems, work with pretty-picture generation via numbercrunching, programming, and putting the head to perform hard intellectual work very often. I can tell no two months from the three years I am working here have been like one another, and the product portfolio keeps increasing.

In my spare-time, I have interest in geospatial stuff, most probably because I like to ride bikes on relatively remote places with maps and GPS, and the very description of geographical stuff allows for a lot of pretty-picturing. Recently, the avalanche of bike-riding GPS data on sites such as Strava, and the current problems CAUSED by traffic-engineering in big cities makes me think these statistical analysis from people displacement's big data can form a body of knowledge for an "anti-traffic-engineering" oriented for actual people instead of private automobiles.

I can "feel" there's a huge future demand, arriving pretty soon, for software tools that transform datasets into useful information. That can happen with medical imaging, geo-statistical imaging, traffic-engineering micro-modelling, and a lot of fields where data collection, transformation, analysis and interpretation is of huge importance, but still needs further development.

I'm not sure I am actually answering your question, but I feel your question is open to some daydreaming, so I hope this helps, and would be glad to answer any comment you may have!