Go for "The Animatrix". Specifically, theThis story titledis told in "The Second Renaissance"The Animatrix is the source you're looking for, specifically, "The Second Renaissance".
EDIT:
This story is the It's a recounting of the events leading to machine uprising, beginning with creation of the fist AI. It's basically expansion on the story Morpheus told Neo, with way more details and an added visual part.
Here's a summary:
In the mid-21st century, humans develop AI. One robot overheard its owner planning for it to be scrapped, and it killed him to prevent this. It was tried and found guilty of murder and sentenced to be destroyed. The rest of AI was sentenced to death as well. Protests and violence, followed by all intelligent robots founding their own city-state called 01. Due to its incredible technological advantage, 01 gained a lot of international manufacturing power. 01 asked to be admitted to the UN. It was denied, and the world decided to destroy it by attacking with nuclear weapons. 01 retaliated and quickly conquered territory. Humanity reacted by blocking out the sun, thinking that the machines only ran on solar power, but the machines were able to adapt.
