Self-trapped beams of light propagate while maintaining their initial intensity profile within a self-induced channel of high refractive index. When multiple self-trapped beams or filaments travel within the same medium, a diverse host of interactions are observed, including attraction, repulsion, fusion, annihilation, and birth. This thesis describes studies of interactions between large and small filament populations and/or beam-induced structures (waveguides) within polymer media. The understanding developed in this fundamental work was applied to design polymer cuboids – the cuboids that count – with computing-inspired functionality. First, the spontaneous self-organisation of randomly-seeded waveguides within a photopolymer material formed the basis of 3 operations: (i) data transfer; (ii) volumetric encoding; and (iii) binary arithmetic. The same material was used for 3D data storage using highly-intersecting waveguide lattices. The pursuit of enhanced capacity prompted an exploration of light coupling in waveguides with small angular separation and significant field of view overlap. Using multiple angled light sources, we successfully demonstrated single-step data writing and multiplexed data reading in these structures. Finally, we examined long-range interactions between 2 to 4 collinear beams within a spiropyran-functionalised hydrogel. The mechanism of refractive index increase in this medium – a light-induced volume contraction and expulsion of water – allowed beams to inhibit their neighbours’ self-trapping, with a clear relationship between number of neighbours and degree of inhibition. These observations were used to form the basis for an optical hydrogel NAND gate. / Thesis / Doctor of Philosophy (PhD)