I got my inspiration from a natural growth with roots "aggressively" digging in to support the "unstable" winding tree above. It is quite definitely linked to the sketch underneath, but I still expanded on the ideas and let the design simply follow.
I was initially baffled as to how to translate a seemingly non connected sketch into 3d. However, after some thought I simply decided to create the gallery space at the zero of the X plane as the ground floor, and so underneath is treated almost as an entirely different building.
What I haven't included in these models, but would be in any further extensions of this design, but would be a central skylight piercing from roof to floor possibly allowing in water as well as light. The water could then be allowed to flow down features of the artists designed for the very purpose. This would create a similar space to an Ancient Roman atrium, and would serve to inspire and provide a space which the staircase could then wind around. To this purpose I have already created the roof leaning into the central point.