Forms Follow Mathematical Functions
The project draws inspiration from Joseph Choma’s book ‘Morphing: A Guide to Mathematical Functions for Architects and Designers’ (2015). Utilizing mathematical functions from the book, it delves into the intricate connections between various shapes and forms and the underlying mathematical concepts. The primary objective is to unveil the captivating relationships between mathematics and design, showcasing the beauty that emerges when precise mathematical principles intersect with creative expression. This exploration seeks to illuminate the profound connections between abstract mathematical ideas and the tangible, visually appealing forms that we encounter in our surroundings.
The mathematical functions were implemented using Rhino Grasshopper, where the code generated all the frames for the animations. Each step in the input values corresponds to a set of points in Cartesian space. These sets, in turn, are employed to construct closed curves, playing a crucial role in defining forms that evolve from simple to complex. The project serves as a visual narrative, demonstrating that the intricate forms found in nature are also a result of inherent functions within biological entities. By employing mathematical functions as a creative tool, the project not only showcases the aesthetic potential of mathematics but also underscores its fundamental role in shaping the beauty we perceive in the world around us.
Form Follows Energy
The project sets out to explore the connection between form and energy. It starts by generating an algorithmic form with Rhino/Grasshopper and simulations were performed using Ladybug, an environmental simulation tool. The form chosen is a twisted tower, which is then panelized. Each panel is extruded into a circle with varying radii, creating a surface with openings and distances from the main frame that change based on simulated radiation values derived from Barcelona weather data.
Simulations are carried out for sunlight hours during the two equinoxes and two solstices. The results are displayed in a legend, indicating the radiation values received by each surface at different instances. The evolution of form and the corresponding radiation values is presented initially from the south and then from the north, illustrating the variations in values based on specific orientations. This iterative process provides a comprehensive view of how the form responds to different radiation conditions, shedding light on the dynamic relationship between the architectural structure and its energy interactions.
Algorithmic Alterations
Every event is a product of specific interactions, just like nature employs varying patterns. The shapes presented below are crafted through an algorithm with distinct stages. Initially, double-curved surfaces are generated to form the foundation. These surfaces then serve as the basis for constructing hexagonal grids. Subsequently, the hexagons within these subsets are scaled and colored based on their distance from the ground. To introduce a bit of randomness and disrupt the orderly color transition in the gradient, the subsets containing hexagons undergo a randomization process. This deliberate variation in the arrangement of hexagons adds an element of unpredictability, contributing to the overall visual appeal and breaking away from a strict, systematic progression in the color gradient.
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