In digital image processing, current methodologies driven by computer vision (CV) and machine learning (ML) principles draw inspiration from the neural processes of the human brain, yet are confined by the technological limitations of existing input and output devices. These typically rely on rectangular or square pixel arrangements to transform real-world scenes into digital imagery. However, the manifestation of hexagonal patterns found in the sensory cells of the human visual system as well as nature itself suggests an efficient evolutionarily motivated alternative. This contribution introduces a novel integration of image processing and ML through the development and evaluation of The Hexagonal Image Processing Framework Hexnet (Hexnet Framework), an open science framework for hexagonal image processing (HIP) and hexagonal deep neural networks (H-DNN). Hexnet aims to bridge the gap between traditional image processing systems and the fundamentally innovative yet nascent potential offered by hexagonal imagery. For evaluation, The Hexnet Hexagonal Image Processing Data Set (Hexnet Dataset) is investigated, emphasizing the benefits of HIP principles in terms of improved image quality, pixel requirements, and classification capabilities, which highlight the possible advantages of hexagonal imagery.