The man, in his early 30s, was first seen on Thursday riding at more than 100mph on the A24 before crashing at a junction with the A27.
He then continued without a helmet around Brighton before crashing at Churchill Square's car park barriers.
Police said it was too dangerous to pursue him at the time without further risk to others.
The man was followed by helicopters but fled on foot. His motorbike, helmet and leather jacket were later recovered.
Officers are now appealing for anyone who recognises him or knows of his whereabouts to get in touch urgently.
The man has a mole on his lower lip and may recently have had his distinctive wavy hair cut, Sussex Police said.
He is thought to have been in the Western Road area near Waitrose at around 18:45 GMT prior to being picked up in an unidentified vehicle.
Hotels, bed-and-breakfasts and other relevant places are being visited and officers are following up further lines of enquiry in Hampshire.
Insp Dave Frey said: "The suspect was riding with total disregard of his own safety and those of others - at excessive speeds, through red lights, manoeuvring around bollards on to the wrong side of the road, and on to pavements in town centres.
"He pretty much contravened every road traffic law and I'm thankful that no one was injured."
Roads policing officer Sergeant Alan Spicer added: "It was too dangerous for patrols to pursue him at the speeds he was reaching without further risk to others.
"He is now believed to be hiding and we would welcome any information from people recognising him or with knowledge of his current whereabouts."
A motorcyclist who rode through Sussex at speeds of more than 100mph, crashing twice, is being sought by police.