Fig. 2.
Inverse design of vegetable, animal, and mineral surfaces. A snapdragon flower petal starting from a cylinder (Left), a face starting from a disk (Center), and the Colorado River horseshoe bend starting from a rectangle (Right). For each example, we show the initial state (top), the final state (bottom) and two intermediate grown states in between. In each state, the colors show the growth factors of the top (left) and bottom (right) layer, and the thin black lines indicate the direction of growth. The top layer is viewed from the front, and the bottom layer is viewed from the back, to highlight the complexity of the geometries. The target shape for each case is given in Inset at the bottom: a snapdragon flower (image courtesy of E. Coen); a computer-render of a bust of Max Planck (model is provided courtesy of Max Planck Institute for Informatics by the AIM@SHAPE Shape Repository); a satellite photo of the actual river bend (image courtesy of Google Earth). The height of the actual snapdragon flower is 30 mm (19), whereas the depth of the canyon is 393 m according to USGS elevation data. (See SI Appendix for animations and details.)