Kingdom:   Plantae
(Unranked):        Eudicots
(Unranked):        Rosids
Order:       Brassicales
Family:      Brassicaceae
Genus:      Lobularia
Species:     L. maritima
Binomial name: Lobularia maritima
Synonyms:   Alyssum maritimum, Alyssum minimum, Clypeola maritima, Koniga maritima.
Common name: Alyssum, Sweet alyssum, Carpet of snow, Sea alyssum, Seaside lobularia, Snowdrift, Sweet Alice, Sweet Alison,

Lobularia maritima is native to northern Africa (i.e. northern Algeria, Egypt, northern Libya, Morocco and Tunisia), the Azores, the Madeira Islands, the Canary Islands and southern Europe (i.e. France, Portugal, Spain, Italy, Albania and Greece). It is now widely naturalized elsewhere in the temperate world.
In New Zealand this prolific self-seeder which is a widely grown as a garden ornamental has escaped cultivation and is now a weed of parks, footpaths, roadsides, waste areas, disturbed sites and coastal environs.
It is an annual plant (rarely a short-lived perennial plant) growing to 5–30 cm tall by 20–30 cm broad. The stem is very branched, with dense clusters of small flowers. The leaves are 1–4 mm long and 3–5 mm, broad, alternate, sessile, quite hairy, oval to lanceolate, with an entire margin.
The flowers are about 5 millimetres in diameter, sweet-smelling, with four white rounded petals (or pink, rose-red, violet and lilac) and four sepals. The six stamens have yellow anthers. The flowers are produced throughout the growing season, or year-round in areas free of frost. They are pollinated by insects (entomophily). The fruits are numerous elongated seed pods rather hairy, oval to rounded, each containing two seeds. The dispersal of seed is affected by the wind (anemochory).
The genus name Lobularia comes from the Greek word meaning "small pod", referring to the shape of the fruits. The name of the species maritima refers to its preferred coastal habitat.

1-Lobularia maritima Sweet Alyssum.JPG

1-Lobularia maritima Sweet Alyssum-001.JPG

Lobularia maritima-001.JPG

1-Lobularia maritima Sweet Alyssum-002.JPG

1-Lobularia maritima Sweet Alyssum-003.JPG

Lobularia maritima-002.JPG

Lobularia maritima-004.JPG

Lobularia maritima-003.JPG 

The above plant pulled out of the ground showing taproot.
Lobularia maritima-003.JPG

Thanks to Wikipedia for text and information: https://creativecommons.org/licenses/by-sa/3.0/