Neuromorphic computing draws inspiration from the brain to design energy-efficient hardware for information processing, enabling highly complex tasks. In neuromorphic computing, chaotic phenomena describe the nonlinear interactions and dynamic behaviors. Chaotic behavior can be utilized in neuromorphic computing to accomplish complex information processing tasks; therefore, studying chaos is crucial. Today, more and more color images are appearing online. However, the generation of numerous images has also brought about a series of security issues. Ensuring the security of images is crucial. We propose a novel fourth-direction hyperchaotic system in this paper. In comparison to low-dimensional chaotic systems, the proposed hyperchaotic system exhibits a higher degree of unpredictability and various dynamic behaviors. The dynamic behaviors include fourth-direction hyperchaos, third-direction hyperchaos, and second-direction hyperchaos. The hyperchaotic system generates chaotic sequences. These chaotic sequences are the foundation of the encryption scheme discussed in this paper. Images are altered by employing methods such as row and column scrambling as well as diffusion. These operations will alter both the pixel values and positions. The proposed encryption scheme has been analyzed through security and application scenario analyses. We perform a security analysis to evaluate the robustness and weaknesses of the encryption scheme. Moreover, we conduct an application scenario analysis to help determine the practical usability and effectiveness of the encryption scheme in real-world situations. These analyses demonstrate the efficiency of the encryption scheme.