Automatic detection of epileptic seizures has been an ongoing area of research for decades due to the complexity and variability of EEG (electroencephalogram) patterns. In this study, we propose a seizure detection algorithm based on a novel feature extraction technique called the Discrete Lissajous Figure (DLF), inspired by classical Lissajous Figures (LFs) typically visualized on oscilloscopes. The method leverages the relationship between the DLF and the autocorrelation function, using the distribution of energy components within the DLF as discriminative features for classifying ictal EEG signals and healthy/inter-ictal EEG signals. Dimensionality reduction is performed using Principal Component Analysis (PCA), and the reduced feature set is then classified using Support Vector Machine (SVM) and K-Nearest Neighbor (K-NN) classifiers for performance comparison. Experimental evaluation on a publicly available EEG dataset shows that the proposed algorithm achieves average accuracy rates between 96% and 100%, comparable to those reported in recent studies using the same dataset.