The article explores chaotic systems similar to the famous Lorenz system, focusing on attractors with distinct shapes. By adjusting a single parameter, these systems can transition from Lorenz-like to Chen-like attractors. The shape of the chaotic attractor is influenced by the instability of certain points within the system. This study reveals connections between the algebraic structure of the system and the geometric patterns of its attractors, providing insights into the dynamics of these chaotic systems.