Thaana, used in the island chain of the Maldives off of the Indian coast, is one of the very very few alphabetic or abugida writing systems whose glyphs (apparently) are not ultimately derived from Proto-Sinaitic. Like most blanket statements on this blog, there are some heavy hedges here.
I said “apparently” because there might have been some influence. It is clear that nine glyphs took their shape from Arabic numerals, and nine from Indic numerals. (Yes, numerals. No, I don’t know why.) The glyphs for those numerals don’t have any obvious relation to the glyphs of the writing systems around them, but it is always possible.
Glyphs for other characters than the base 18 — mostly for loan words — are made by adding diacritics to those base glyphs. Finally, there is a “y” character, and nobody knows what glyph, if any, was its inspiration.
Thaana is an abuguida, where vowels must always be attached to a preceding consonant with diacritics. There is a special character, the alif, which is a “null consonant”, existing only to hang solo vowels upon. Interestingly, the diacritics are derived from Arabic vowel points, not from any of the Indic diacritics.
Thaana displaced Dhives Akuru gradually in a period when the Maldives were becoming more Islamic. It was originally used to write magical incantations, which might be why numbers were used for letters — perhaps it would be better understood as a code.
In the 1970s, telex machines were installed in government offices, and the new communications technology was seen as highly beneficial. However, the telex machines only used Latin script. A Latin transliteration script was developed, and (despite it not fitting the language well) was popularized. Thaana almost died out then, but it was reinstated in 1978; both Thaana and Latin are now used.