Parallel programming remains one of the most challenging aspects of High-Performance Computing (HPC), requiring deep knowledge of synchronization, communication, and memory models. While modern C++ standards and frameworks like OpenMP and MPI have simplified parallelism, mastering these paradigms is still complex. Recently, Large Language Models (LLMs) have shown promise in automating code generation, but their effectiveness in producing correct and efficient HPC code is not well understood. In this work, we systematically evaluate leading LLMs including ChatGPT 4 and 5, Claude, and LLaMA on the task of generating C++ implementations of the Mandelbrot set using shared-memory, directive-based, and distributed-memory paradigms. Each generated program is compiled and executed with GCC 11.5.0 to assess its correctness, robustness, and scalability. Results show that ChatGPT-4 and ChatGPT-5 achieve strong syntactic precision and scalable performance.