<p>Nonlinear activation functions are the critical factors for Hopfield neural networks (HNNs) to exhibit dynamical behaviors. To this end, a novel two-dimensional (2-D) seed map is proposed based on the two-neuron HNN framework with torus and sine activation functions, which can produce multi-tongued hyperchaotic attractors with high performance indices. Thereafter, by coupling two state controllers with the proposed seed map, a four-dimensional (4-D) grid hyperchaotic map is constructed to generate hyperchaotic attractors with grid distribution and grid coexistence. On this basis, a universal color image encryption algorithm suitable for the grid hyperchaotic map is developed. It should be highlighted that this algorithm makes full use of the grid attractor features and combines the grid distribution attractor and the grid coexistence attractors with the permutation and diffusion of the image encryption algorithm respectively. Numerical simulations and performance tests demonstrate that the developed algorithm exhibits strong resistance to attacks, high security, and reliability, making it suitable for practical image encryption applications.</p>