The Gaṇeśa Purāṇa as well as the Mudgala Purāṇa refers to धुम्रवर्ण गणेश (dhumravarṇa gaṇeśa) and धूम्रकेतु गणेश (dhūmraketu gaṇeśa). That is a smoky or ash-coloured Gaṇeśa (which is associated with bhasma), so this form is deeply connected to Goddess Dhūmāvatī. The Mudgala Purāṇa lists eight forms of Gaṇapati and the last of them is धुम्रवर्ण गणेश (dhumravarṇa gaṇeśa). There is a mention of another form in the Gaṇapati Purāṇa, one of the four, which is called धूम्रकेतु गणेश (dhūmraketu gaṇeśa). The first form is called महोत्कट विनायक (mahotkaṭa vināyaka) and manifests itself in the satya yuga, the form मयूरेश्वर विनायक (mayūreśvara vināyaka) is manifested in the tretā yuga, गजानन (gajānana) – in the dvāpara yuga, and धूम्रकेतु विनायक (dhūmraketu vināyaka) – in the kali yuga. It is completely normal for different forms of Gaṇapati to be worshipped at certain time periods. That is traditionally performed every month at chaturthi tithi, according to the Indian almanac (pañcāṅga).
1. In the month of Māgha, भालचन्द्र गणेश (bhālacandra gaṇeśa) is worshipped.
2. In the month of Phālguna, हेरम्ब गणेश (heramba gaṇeśa) is worshipped.
3. In the month of Caitra, विकट गणेश (vikaṭa gaṇeśa) is worshipped.
4. In the month of Vaiśākha, वक्रतुण्ड गणेश (vakratuṇḍa gaṇeśa) is worshipped.
5. In the month of Jyeṣṭha, रथ गणेश (ratha gaṇeśa) is worshipped.
6. In the month of Āṣāḍha, लम्बोदर गणेश (lambodara gaṇeśa) is worshipped.
7. In the month of Śrāvaṇa, विनायक गणेश (vināyaka gaṇeśa) is worshipped.
8. In the month of Bhādrapada, एकदन्त गणेश (ekadanta gaṇeśa) is worshipped.
9. In the month of Aśvīna, कृष्ण गणेश (kṛṣṇa gaṇeśa) is worshipped.
10. In the month of Kārtika, पिंग गणेश (piṃga gaṇeśa) is worshipped.
11. In the month of Mārgaśīrṣa, गजानन गणेश (gajānana gaṇeśa) is worshipped.
12. In the month of Puṣyā, लम्बोदर गणेश (lambodara gaṇeśa) is worshipped.
In general, according to the Gaṇeśa Purāṇa, धूम्र गणेश (dhūmra gaṇeśa) is worshipped. He is described with a vāhana in the form of a blue horse, which differs from the common popular version where he has a vāhana in a form of a mouse. In this form he is associated with Kalki-avatār, a form of Viṣṇu. However, we must bear in mind that in India, followers of different Sampradāyas may see their principal Deity as the highest. So it is not surprising that for some of them Viṣṇu is a manifestation of Śiva, for some – Viṣṇu and even some forms of Śiva are manifestations of the Mother Goddess, and that is also true for the worshippers of Gaṇapati. Dhūmra Gaṇapati is therefore a form of Gaṇeśa, which is the counterpart of Kalki-avatār in Vaishnavism. Although, there are ślokas describing Dhumravarṇa Gaṇapati sitting on a mouse (आखु / ākhu):
आखुवाहन एवासौ शिवात्मा तु स उच्येत ।।
ākhuvāhana evāsau śivātmā tu sa ucyeta ।।
The avatāra who has the smoky colour, the one who is also the destroyer of abhimanasura (the demon of pride). The one whose means of transport is in the form of a mouse, who is actually to be called the essence of Śiva.
Accordingly, it is very common in India to reduce all individual forms of Gaṇeśa or some other Deity to the most popular forms and their attributes at first. And then, to the yogic experience in general, as for example, in the Nātha-sampradāya, where Gaṇeśa has a human face, not an elephant-headed one. That is not because he originally had a human face before Śiva gave him an elephant’s head in the famous story. It is simply that for a yogin the human form is closer and the aim of all practices is to realise the divinity in own body, which is what all practices in tantrism lead to. The aim of realisation of a particular mantra (which is one with its Deity) is that your whole psychophysical being becomes a permanent carrier of the reality of that Deity. Continuous total abiding in God means eternity – the nature of ātman, which is the goal of yoga. However, Dhūmra Gaṇapati, like Goddess Dhūmāvatī, is the symbolic end of the spiritual path. It is a symbol of the burned-out worldly aspirations (saṃskāra), the residing of consciousness in the mundane (vāsanā), and in general – of the fire of any passion for life (kāmāgni). The worldly man is constantly engaged in a bubbling life full of fire, the last sign of which is the smoke of the funeral pyre, it’s grey ashes (bhasma). He who has forsaken all the useless fuss of the world, strives for the silencing of all ‘vṛitti‘ (the endless cycle of thoughts) in the mind. Such a devotee strives unceasingly towards the eternity of his true Self (ātman), seeing all worldly things transformed into the nectar of bhasma, the symbol of emptiness from which all forms, all activities (‘pravṛitti’), have emerged. Such yogins are in no hurry to go anywhere. Even if they do stay in this world, they are in a very nominal contact with everything. Dhūmra Gaṇapati and Dhūmāvatī properly represent the nature of Ketu and Śani in jyotiṣa. Śani is the slowest of all planets, so it constrains the exaggeration in our activities, the same is with Ketu. But these grahas could be helpful to those who choose discipline and aspiration towards mokṣa.