Motivated by a diversity of the shape instability phenomena in condensed matter physics, we study formation of elastic ribbon structures and trans-formation into helicoidal structures. Using the multi-pulse laser-matter interaction with the Co-coated surface, a one-dimensional high-density vortex filament array has been created. Increasing the number of pulses, the oscillatory strain field causes the cascade of the shape transformations into structures of increasing topological complexity:vortex filaments into ribbons, into ribbon-helicoids and tubular-ribbon-helicoids, and then into short ribbon-structures with the complex Scherk surface being identified. Above a critical number of pulses, the system is catastrophically disintegrated into small-scale wrinkled and crumpled surfaces. |