A completely folding bike

The trend of folding bicycles is growing, due to urbanization, high density of people inside cities and the wheel to reduce pollution (yes, it is a pun). There are many types of foldingbicycles but they all have one thing in common: the wheels are not folding. If you look at pictures of folding bikes you'd notice one of two things: either the wheel dominates the size of the folded bikes, such that you see a large circle with some bars and hinges attached to it; or the bike's wheels are very small, reduced in size exactly because of this problem.

On the other hand, wheelchairs have progressed much more due to the large demand and the subsidized market. In this unique apparatus, the concept of folding wheels is now possible, with several competitors out there. 

Why not combine the two? Why not enjoy the world of folding bikes as well as folding wheels, to reduce even further the size and complexity of the bikes to a minimum? This can be done, while still enjoying the benefits of a large wheel.

And while we're contemplating "revolutionary" ideas on folding and bikes, why not do it an automatic unfolding and folding? The idea of inserting some kind of engine into the design to supply the power for the transformation is prohibitive, since then the bike will need battery, and the complexity and weight will dramatically increase. However, there are other possibilities. One can be taken from the simple idea of a folded springy ring, that are ubiquitous in IKEA children toys. Is there a possibility to construct a formidable bike from springy materials that can then carry the weight of a person on them? 

The design of new materials is reaching a turning point where flexibility and hardness can transformed with a turn of a switch Maybe using such materials and concepts from folded wheelchair's wheels one can created a truly and wholly folded bicycle that can be carried in your purse.