How were vibrant colours achieved during the reign of Tutankhamun?

Tutankhamun reigned around 3000 years ago (1336-1326BC). You'd expect that the things that were produced at that time would have some colour but would not be vibrant. Visiting the Tutankhamun: Treasures of the Golden Pharaoh exhibition at the Saatchi Gallery gave me a completely different idea about what colours were like 3000 years ago.

Obviously artificial colourants were not invented and would still not be invented for thousands of years, so the only way these vibrant colours could be achieved during his time was by using natural materials.

Within the objects found in the tomb of Tutankhamun, the most frequently used materials were wood (especially ebony and red wood) , gold leaf, faience and alabaster. Other ones used were:

And these are only the ones that were showcased at the exhibition which only included 150 objects from the 5,398 found so that list of materials would probably get longer if all of the things found were considered.

Below you can see what colour is achieved with what material as well as some of the colourful objects from Tutankhamun's tomb.