It's something I read back in junior high, 20 years ago or so. The cover had this yellow spaceship zooming over a planet on it.
The only bit I can remember story-wise is some story dealing with the winding down of 'life', I guess, and the one part about a spider that could see in the gamma spectrum and spun fibres of neurons when it needed to think more.
It was an anthology, in English, might have been written in the 50's as it dealt with radiation.
The story that mentions the spider is The Voices of Time by J. G. Ballard. The part of this story describing the spider is:
Coma was peering through the window of the next cage and pulling an unpleasant face. Over her shoulder Powers saw she was watching an enormous spider-like insect, as big as a hand, its dark hairy legs as thick as fingers. The compound eyes had been built up so that they resembled giant rubies.
'He looks unfriendly,' she said. 'What's that sort of rope ladder he's spinning?' As she moved a finger to her mouth the spider came to life, retreated into the cage and began spewing out a complex skein of interlinked grey thread which it slung in long loops from the roof of the cage.
'A web,' Powers told her. 'Except that it consists of nervous tissue. The ladders form an external neural plexus, an inflatable brain as it were, that he can pump up to whatever size the situation calls for. A sensible arrangement, really, far better than our own.'
Coma backed away. 'Gruesome. I wouldn't like to go into his parlour.'
'Oh, he's not as frightening as he looks. Those huge eyes staring at you are blind. Or, rather, their optical sensitivity has shifted down the band, the retinas will only register gamma radiation. Your wristwatch has luminous hands. When you moved it across the window he started thinking. World War IV should really bring him into his element.'
However I can't think what the anthology could be. I read the story in Ballard's anthology The Four Dimensional Nightmare, but that isn't themed about radiation and doesn't have a cover matching your description. The ISFDB entry for the story lists all the anthologies the story is known to have appeared in, but none them look like a match for your description.
