In 1402 the Byzantines were defeated at Ancyra by the hordes of Tamerlane. They were saved when he turned back from his conquest to invade India where he died in 1405. In the period of recovery that followed the Byzantines started sending explorers further afield.
The Early Discoveries
In 1428 Konstantin Zapatos, the emperor's Imperial Seamaster, landed on the coast of North America. The land he found was heavily wooded and inhabited by strange, spirit worshipping natives. After two years of attempting to peacefully 'educate' the locals a fierce revolt broke out that killed most of his men. He came to the conclusion that the land was not desirable and colonising it would not benefit the Byzantine Empire. So he left it to be colonised by later explorers such as Sir Walter Raleigh of England.
On his next expedition, in 1431, Konstantin headed southwest and discovered a shallow sea full of glorious tropical islands that he named the Caribbean, after the locals, the Caribs. He made a settlement on the largest island, New Crete, and sailed back to Constantnople in 1432.
The Empire Expands
Over the next 50 years, large sections of the world were colonised by the Byzantine explorers. Much of Africa's west coast and the Caribbean became cluttered with small settlements full of Greek immigrants seeking a new life. Sailors setting off from Egypt through the Red Sea arrived in India and in 1470 Michaelos Paolaegios sailed around the Cape of Good Hope and discovered the passage to India. In order to reduce journey times, Emperor Alexander VII ordered the construction of a waterway through the Sinai Desert from the Mediterranean to Suez on the Red Sea. In 1491, Michaelos Paolaegios II, the great explorer's son, landed on the coast of what will become New Byzantium and made contact with the Aztecs.