I happened to come across a photo of a similar leafless shrub (without flowers) that also had 120 degree branches and looked thorny, or Spiny is probably a better description. It helped me to identify the plant in your photo as a Launaea arborescens. It is an unusual species of Chicory in the dandelion family, Asteraceae. Being tolerant of arid locations, it native to northwest Africa and southern Spain.
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