देवेषु विश्वासटिप्पन्यः

Source: TW

A rendering of the manifestation of supreme shakti navAtmikA of the pashchimAMnAya. The Agama explains the emergence of the navAtmikA form thus in the teaching of umA to shiva:

शशाङ्कार्ध-कला ज्ञेया
अम्बिका मध्यचन्द्रिका । एका एव पराशक्तिस्
त्रिधा सा च प्रजायते ॥

The goddess ambikA manifest in the midst of the half-moon triplicated herself (technically the central triangle of the yantra). This triad of goddess are the shakti-s vAmA, jyeShThA and raudrI, corresponding to the first 3 deities of the vAmadeva-brahma-mantra

एभ्यो युक्त-वियुक्तेभ्यः
संजाता नव-वर्ग-जा ।
नवधा च त्रिधा सा तु
नव-वर्गाक्षमालिका ॥

These 3 combine and disjoin i.e., 3 x 3 to birthing her 9 fold form. She of 9 & 3 fold forms is the 9 fold rosary of Sanskrit letters. This latter reckconing while differing among teachers, can be interpreted thus: 1 vowels; 2-6: velar, palatal, retroflex, dental, labial consonants; 7 half-vowels; 8 sibilants; 9 aspirate.
When they are all expanded, she becomes the 50-fold mAlinI of the pUrvAMnAya. These letters are said to form the basis of 5-brahma-s

पञ्च-मन्त्र-गता देव
सद्यादीनां यथाक्रमम् ।
तेन सा पञ्चधा प्रोक्ता
ज्ञात्वया सुरनायक ॥

She manifests in order as the 5 mantra-s starting with sadyojAta; that is 5-fold form.
The tantra also describes her as assuming other forms: the 4 fold form is said to be that of chaturbhaginI-s the goddesses of the vAmasrotas.
Then she also assumes the form of the 11 rudrANI-s who go back to the yajurveda, famously invoked in the aruNaketuka-chayana.

However, in the bhairava-srotas they have special significance related to the explosive kuNDalinI arousal

तेन तेन क्रमेणैव
रौद्री-भावम् उपागता । कन्दाधार-पुरस्था तु
धुननावेशनी स्मृता ॥
कम्पनी रौद्री विख्याता
घूर्णणी उद्भवात्मिका । एकाङ्ग-नर्तनीत्य् आख्या
अश्रुपाती कुरङ्गिणी ॥ सिंह-शब्दी पुलिन्दी च
एकादश प्रकीर्तिताः । रुद्रभागे स्थिता ह्य् एते
द्वादशान्ते लयं गताः ॥

The 11 rudrANI-s:

kandAdhAra-purasthA: the one residing in the mUlAdhara;
dhunanA: the shaking;
AveshanI: causing various signs of possession.
kampanI: trembling;
ghUrmaNI: causing whirling around;
udbhavAtmikA: causing upward levitation/ rising to higher levels of perception;
ekA~nga-nartanI: dancing on one limb
ashrupAtI: causing tears to flow;
kura~NgiNI: causing leaping like an antelope;
siMha-shabdI: causing roaring like a lion;
pulindI:-> vision of subterranean realms

Interestingly, 2 of the 12 kaumAra-mAtrR^i-s in the bodhAyanokta-skanda-yAga are named AveshinI & ashrumukhI, paralleling the rudrANI-s of this list.