When he was five years old, Felix Baumgartner drew a picture for his mum. Twelve years later, when the first man to break the sound barrier unaided had just made his first ever skydive, Baumgartner's mother gave the picture back to him: it showed him floating down to earth, suspended – horizontally, but you can't have everything – from a large parachute. There's a happy, smiling sun beaming down on the scene, and what looks like his family standing on the ground, with drinks, waiting for him to land.

Tom Daley, who became a world diving champion at the age of 15 and has represented Great Britain at the last two Olympics, similarly prefigured his achievement, drawing a picture of himself aged nine. Titled My Ambition, the drawing, which he tweeted after winning a bronze medal in the individual competition this summer, shows him in a handstand on a diving board, with the Olympic rings and the words "London 2012" on either side (London was, at the time, just one among several candidate cities).

Psychologists have long known that art created by children can be an accurate reflection of their inner worlds. Children create art for the same reasons as anyone: to express thoughts or emotions. Art can provide them with a safe environment to delve into their memories and negotiate present-day realities, telling a story that that can capture a moment – or a sequence of moments – in their physical, emotional or psychological life.

Much of the attention paid to the interpretation of children's art in recent years has tended to concentrate on its role in "understanding negative events", says Dr Esther Burkitt, reader in developmental psychology at the University of Chichester, a specialist in the field who has published widely on many aspects of children's drawings. Painting and drawing can help children in psychological distress to confront issues such as trauma, depression or abuse, and allow therapists to help them externalise and discuss problems.

Children's terrifyingly simple, brutally clear drawings of war and atrocity have been extensively used to help young victims recover from the traumatic experiences they have lived through with their families, and even have been accepted by the International Criminal Court as supporting evidence of violations of the rules of war.

It is rarer, says Burkitt, to see a more positive representation of images created by children. "But children's drawings of themselves can, certainly, be representative of their hopes and dreams," she says. "And the act of focusing and visualising can help them to realise their dreams. The act of drawing can be about ambition and value clarification: helping children to crystallise a particular goal, to really focus and go on to achieve what they want to become."

While we should be wary of predicting on the basis of a drawing, "it's pretty amazing that we can make these links back," Burkitt adds. From where we are now, drawings such as Baumgartner's and Daley's seem to "show incredible foresight, but also the sacrifices they might have made. They can certainly be seen as representations of vision and motivation".