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In recent decades, the search for new geometrical innovations has been of great interest for contemporary architects artists, trying to escape the repetitive use of historical ornamental details of architectural styles orders or the absence of such ornaments in the modern style.  This paper aims to lay down the basis for generating new muqarnas elements based on the cosmological nature of Islamic Architecture, but still preserving its concepts. The muqarnas was chosen because it is one of most original inventions of Islamic architecture and one of its most effective and widespread applications. Innovation in its design requires freedom of expression that can be limited by design software. Furthermore, the process of testing ideas can be tedious and time-consuming. Parametric and generative design, using Grasshopper, is used to reformulate the muqarnas generation process using visual programming. Parametric design and hypothetical geometric patterns in a linear or polar arraying direction produce a clearly defined muqarnas.