I want to create a page in Magento that shows a visual representation of the categories.. example
CATEGORY
product 1
product 2
ANOTHER CATEGORY
product 3
Hey something like this might help you, I've adapted it slightly to answer your question more specifically.
$h3h3=Mage::getModel('catalog/category')->load(5); // YOU NEED TO CHANGE 5 TO THE ID OF YOUR CATEGORY
$h3h3=$h3h3->getProductCollection();
foreach($h3h3->getAllIds() as $lol)
{
$_product=Mage::getModel('catalog/product')->load($lol);
print $_product->getName()."
";
}