Blue or reticular veins.
The veins in your pictures are called blue or reticular veins and are not varicose veins. There are many reasons for vein formation with common causes being genetics, pregnancies, hormonal, aging and sometimes there is no reason. The best thing for you to do is to see a vein specialist for a full venous evaluation with a venous reflux ultrasound. This will help to determine the status of your veins and your options for treatment and prevention.
New Onset Varicose Veins
There are many causes for the development of varicose veins - weight gain, hormones (birth control pills), recent oregnancies or just good old genetics. If your father had vein problems (venous insufficiency), you are likely to have them. More so thanif your mother has venous insufficiency. Venous insufficiency is a problem with vein valves and initially it manifests itself as symptoms only (aching, pain in the legs, heavy legss, tired legs, itching in the legs, cramping or throbbing in the legs, leg or ankle swelling at the end of the day) and as time goes on, varicose veins and spider veins form. You may well have venous insufficiency and this can be looked for by a Duplex vein scan (venous Doppler) and you should seek a vein specialist - one who has boards from the American Board of Venous and Lymphatic Medicine and they are most likely to have all of the different techniques available to treat this problem - EVLT or VNUS Closure or ClariVein as well as expertise in dealing with the varicose veins that you show with foam sclerotherapy. Read ebooks about venous disease on the link below and good luck - what you have is very easy to treat. Get it treated before they proliferate. I would also take some bioflavonoids or horse chestnut supplements to help prevent more venous disease.