Hierarcy Query Mysql
If the depth of tree is limited to 3 (case of your sample). You can do like this.

(SELECT t1.* FROM tree AS t1 LEFT JOIN tree AS t2 ON t2.parent_id = t1.uid LEFT JOIN tree AS t3 ON t3.parent_id = t2.uid  WHERE t1.parent_id = 1) 
UNION
(SELECT t2.* FROM tree AS t1 LEFT JOIN tree AS t2 ON t2.parent_id = t1.uid LEFT JOIN tree AS t3 ON t3.parent_id = t2.uid  WHERE t1.parent_id = 1)
UNION
(SELECT t3.* FROM tree AS t1 LEFT JOIN tree AS t2 ON t2.parent_id = t1.uid LEFT JOIN tree AS t3 ON t3.parent_id = t2.uid  WHERE t1.parent_id = 1);


My solution don't respect DRY principle but this is the only simple solution that I found for now.

If you don't know in advance the maximum depth of your tree please check following questions and links that discuss the subject :


https://stackoverflow.com/questions/5688376/mysql-select-tree-parent-ids
https://stackoverflow.com/questions/18083546/mysql-recursivetree-parent-child-category
http://mikehillyer.com/articles/managing-hierarchical-data-in-mysql/


Hope this help!