The word swastika is Sanskrit and means "the self-manifested mark."  In other words, it is a sign of self-realization.  It is undoubtedly related to the wheel or dharmachakra, but the fact that it is not wholly enclosed by a rim indicates a  potential for openness and movement.

Pundit Ravi derives the word from su (well), asti (is) and ka (noun ending,) -- "it is well."   He says that the right-turning mark is male and the opposite is female, associated with Hindu goddess Kali and considered inauspicious.

 Like e.g. the serpent, the swastika crystallizes fundamental principles relating to natural universal processes and their relationship to terrestrial life and was designed to evoke an intuitive or emotional response rather than an intellectual understanding.

As the serpent is the symbol of the creative, energizing force of the Supreme Spirit, the swastika is representative of that life-force being set in motion to initiate the cyclic workings of nature. Both images are thus closely inter-related.

 The ancient Vedic seers described the original cosmic creative process as `the churning of the milky ocean' whereby fields of subtle substance become condensed into gross matter; a view that is now widely accepted today in energy-field physics research.

 This `churning' is represented geometrically in Tantric ritual as a four armed cross within a circle and the cross is meant to be imagined as oscillating backwards and forwards as in a churning motion. The forward movement clockwise is towards evolution while the anti-clockwise movement is towards dissolution. The circle represents the universe in its potential un-manifested state prior to creation and is called in Hinduism `Brahmanda'. The Aryas also believe that the universe periodically dissolves and is then re-created. The period between dissolution and re-creation is known as `Pralaya', a time of rest between creative periods. A period of creativity is called `Manvantara' and both periods (i.e. creation and dissolution) constitute a `Kalpa' or a cycle of creation. The dissolutionary process due to the inevitable pull of gravity and a slowing down of the expanding evolutionary process has been labelled by Western cosmologists as `the big crunch'. The entire creative process is again more descriptively labelled by the Aryas as `the breathing out of Brahma' (the Creator in the Hindu Trinity) while the dissolutionary process is seen as `the breathing in of Brahma'. This cyclic process of cosmic, periodic, involution, evolution and dissolution is symbolized by the forward and backward movement of the cross.

The four arms of the cross are known as `the four arms of Vishnu', the Supreme Deity in Vedic times who later became the `preserver' in the Hindu Trinity. Vishnu's role is to maintain order, balance, and cohesion throughout the created universe. This is the `mystic cross' which later found its way into all religions with certain modifications as the Egyptian Cross, the Chinese Tau, the Cross of the Rosicrucians and the Christian cross.

The created is sustained by continual opposition between two forces, i.e. attraction and repulsion which act and react via a process of flux that is mirrored in the activity of all nature from the breathing of plants, the action of the human lungs, bio-rhythms, the flow of energy in a dynamo, to the expansion and contraction of the Earth itself.

 It is the oscillating motion of the cross within the circle which symbolizes that opposition between positive evolutionary forces and negative dissolutionary forces that give birth to the swastika in both its configurations, i.e. right-angled or left-angled.

 The whole of creation is bound by this principle and by the ultimate balancing of these two polarities, `well-being' that is an ideal state without conflict, may be achieved. On a personal level, this ideal condition, as any individual knows, may at its best be only a sometimes thing during the course of day to day living. The point of eventual neutrality or perfect balance between the two forces, is equilibrium -- thereby no existing conflict between negative and positive. If it were to become an actual consistent condition, the very purpose of life itself (which is innately felt by most individuals as growth towards an ideal or perfection, or total `order') would be pointless and the evolutionary process would cease to be of significance. The cross at rest symbolizes that final perfect balance or equilibrium -- Pralaya.

 On Siva temple throughout India the right-angled swastika is ever present which indicates the transforming and evolutionary aspect which Lord Siva represents in Hindu philosophy.