The paramedian reticular nucleus (in Terminologia Anatomica, or paramedian medullary reticular group in NeuroNames) sends its connections to the spinal cord in a mostly ipsilateral manner, although there is some decussation.
It projects to the vermis in the anterior lobe, the pyramis and the uvula.
Lesions in the paramedian reticular nucleus have been shown to cause a stereotyped increase in the random patterns of motion in rats.
It seems possible that the random motion patterns of the above rats were caused by an inability to mediate their horizontal eye movements.
This article incorporates text in the public domain from the 20th edition of Gray's Anatomy (1918)