MySQL - Query combine rows with same id and keep all entry for that id but as one record

I have been working on a table in a mysql database being hold locally on a wamp server I am using the phpmyadmin area with in wamp to run the querys. I am trying to get the data to do the following:

Can anyone help I have a table with a number of records for plants. A plant can have a number of names the table shows this as different records. The table is called new_plantsname

plantid name
1       tree
1       rose
2       bush
3       tree
3       bush
3       rose

this continues for over 3000 records

what i want is it to combined records with same plantid and show the different names in different columns:

plantid name1 name2 name3 ...
1       tree  rose  NULL
2       shrub NULL  NULL
3       tree  rose  bush 

etc

From a glance I believe a plant has no more than 4 names.

Can one help me the query to do this. I also want to save results to a new table

Someone has given me the following for the answer:

select plantid,
  max(case when nameRn = 'name1' then name end) Name1,
  max(case when nameRn = 'name2' then name end) Name2,
  max(case when nameRn = 'name3' then name end) Name3,
  max(case when nameRn = 'name4' then name end) Name4
from
(
  select plantid, name,
      concat('name', @num := if(@plantid = `plantid`, @num + 1, 1)) as nameRn,
      @plantid := `plantid` as dummy
  from
  (
    select plantid, name, @rn:=@rn+1 overall_row_num
    from yourtable, (SELECT @rn:=0) r
  ) x
  order by plantid, overall_row_num
) src
group by plantid;

This seem to work while no errors but it didnt combine the records it only kept the name of the first record with the id not the rest. DATA USED:

plantid     name
    1       tree
    1       rose
    2       tree
    3       rose
    3       bush
    3       rose

RESULTS:

mysql sql phpmyadmin wampserver