Amytrophic lateral sclerosis (ALS) is an incurable neurodegenerative disease. Difficulty articulating speech, dysarthria, is a common early symptom of ALS. Detecting dysarthria currently requires manual analysis of several different speech tasks by pathology experts. This is time consuming and can lead to misdiagnosis. Many existing automatic classification approaches require manually preprocessing recordings, separating individual spoken utterances from a repetitive task. In this paper, we propose a fully automated approach which does not rely on manual preprocessing. The proposed method uses novel features based on fractal analysis. Acoustic and associated articulatory recordings of a standard speech diagnostic task, the diadochokinetic test (DDK), are used for classification. This study's experiments show that this approach attains 90.2% accuracy with 94.2% sensitivity and 85.1% specificity.