Programmable surfaces and structures are mechanisms that transition between two or more geometric configurations. Programmable surfaces capable of altering their topology with a change in operational conditions have the potential to enable a wide range of applications in a variety of domains like haptics, wearables, human-computer interactions, fluidsurface interactions, and shape morphing structures. Prior research on programmable surfaces has developed various techniques to realize shape change applications. 4D printing includes multi-material printing of mechanisms that transform from any 1D or a 2D shape into a 3D shape using simple energy inputs like heat, water, or light. Additionally, origami composite structures with selective actuation of shape memory polymers also afford complex shape changes. We present a novel approach to designing programmable surfaces by incorporating shape memory alloys (SMA) and textile manufacturing processes to form variable topology programmable surfaces from knitted active textiles. Thermally responsive shape memory alloys (SMAs) leverage solid-state phase transformations and the shape memory effect to return the material to a predetermined state upon heating. The shape memory effect enables creation of multi-stiffness SMA configurations that can be utilized to develop structures with tunable surface topographies. Active knitted textiles act as programmable surfaces by transforming from an inactive 2D flat surface in the cold, flexible martensite state into active 3D surfaces when heated above the austenite finish transformation temperature.