For that, you first have to cut the query string. Try the following:
$ArrayOfWords = explode(" ",$TheQueryString);
Then in your case, $ArrayOfWords would contain the following:
$ArrayOfWords[0] = "pink";
$ArrayOfWords[1] = "fat";
$ArrayOfWords[2] = "dog";
Then, you can extend the query using these parameters. Take a look, thought, that there must only be one space between words, or else, one of the array elements might contain an empty value, and, when making a query with LIKE an that argument... it would be a query like this:
SELECT field FROM table WHERE field LIKE '%%'
And that returns all of the records in the table. Try to check if any of the values from the Array is equal to nothing,m and, if so, don't use it as an SQL criteria.
Hope this helps
fLIPIS