The painter Howard Hodgkin has one of the world's finest collections of Indian art from the Mughal period and here, for the first time, he shows the entire visual feast to the public. In the early 16th century the Mughal emperor Babur extended his rule from Afghanistan into northern India. He and his dynasty were Muslims, and they brought the traditions of Islamic art into India. Manuscript illumination and miniature paintings were arts that reached superb heights in Persia from the 13th century onward. In India, the Mughal rulers imported such skills as they delighted in superbly detailed portraits, fantastic scenes from legend and history, and the depiction of nature in scintillating colours.  Hodgkin has said he does not look for particular iconographic or historical topics in this rich artistic territory, just for "great art". And he should know how to recognise it.  The connections between Mughal art and his own painterliness may seem so obvious they do not need pointing out. Hodgkin is a poet of colour, and the Indian paintings he collects abound in intense, non-naturalist colours. You can clearly see how an artist who loves to create a great wave of green or a flame of red might love pictures that explode with untamed colour. Another similarity is in scale: while Hodgkin makes paintings of all sizes he often excels with particular feeling in small, intense works that share the contained boundaries of small Mughal pictures. And finally there is accuracy. These paintings are meticulously precise – as if done under a microscope. And while Howard Hodgkin has a free and bold manner, the passion and conviction of his paintings comes from precise memories of places, people and times.  An impressive collection; a wonderful artist.  • Ashmolean Museum, Oxford until 22 April  Yayoi KusamaSpots, spots, spots in the art of this painter, installationist, and Japanese icon.• At Tate Modern from 9 February  Andrea ZittelUtopian experiments in living from a contemporary answer to Josef Beuys.• At Baltic, Gateshead from 10 February  Joan MitchellLast works of a splendid American painter.At Hauser and Wirth, London until 28 April  Giovanni Bellini's Doge Leonardo Loredan, 1501-2  The Doge of Venice was an elected official with the charisma of a monarch – an idea that survives in the American presidency. Like America, the city state of Venice was a republic, but unlike American presidents, once chosen, Doges ruled for life. From the early middle ages until the age of Napoleon Venice was independent, rich and powerful. And throughout that time the Doges embodied the state that called itself the "Serenissima".  No portrait in the world is more serene than Bellini's Doge Leonardo Loredan. He has the grace of a male Mona Lisa. Blue air enfolds him. His silk garb epitomises the wealth and luxury of Venice, and the light on his face is so beautiful, so subtle, it is as if he were standing on the balcony of the Doge's Palace watching a sunset. Artists portrayed all the Doges for centuries, and this is simply the finest and most exquisite of all those paintings – a masterpiece indeed.  The softness of skin, the delicacy of temperament – that tender look in his eyes – and the indefinable calm of the painting's atmosphere are captivating: the sculpted formality is majestic. This is a portrait of a unique kind of authority, the power and also the tempered care of a ruler of a republic, first among equals. If Caesar projected an image like this no one would have assassinated him. Compared with Venice, the Roman republic was just a flash in the pan. Bellini has painted one of the greatest political portraits in all the world.  David Hockney followed the reaction to his Royal Academy show on Twitter  Moscow has its very own answer to Banksy  How Leonardo da Vinci's work compares with that of his pupils  The link between Florida street art and Renaissance Florence  How Rodin's sculptures inspired a hip-hop dance  Sign up for the Art Weekly newsletter
Jonathan Jones: Hodgkin's impressive Mughal art collection explodes with untamed colour, much like his own work, while a Japanese icon hits the spot at Tate Modern – all in your weekly arts roundup