Field Lines

Field lines are invisible in the final image but their construction is necessary for the location of 1-DE s In the image below a set of vertical dots have been placed 10 units apart along a vertical field line which is parallel to the vertical edge of the frame. A second set of dots extend along a field line which subtends the horizontal frame at about 20 degrees. the two dots immediately below and to the right of the dot in the top left corner control the position of the blue dot so that a distance of 10 units is maintained between them and the blue dot. The distance between dots correlates with the trellis rule such that dots in the same field line will always be at constant separation.even though the trellis is scissored open or shut. The general equation for dealing with straight field lines in this manner. Where H is constant And Y1 & X2 are co-ords for related dots. [X3 , Y3] = [(H2 - Y21)1/2 , (H2 - X22)1/2] gives us the position of the next dot in the row.

More complex fields can be set up by interfering field lines derived from sine or parabolic functions.A simple parabolic curve ¦ (x) = x2 can be made to interfere with itself at varying phase angles and at varying directions to produce some quite remarkable field lines

The two lower fields show not only the grid spacings and phase relations of interfering waves but now they are at the second stage of creation since representational lines have been added. The lines merely indicate the angular relationship of that part of the field to its centre. Later on 1-Dimensional elements (1-DEs) are overlayed where the 'representational lines' are. (See Artworks)

The general equation for evaluating line integrals is of the form ? ¦ x(s), y(s)]ds

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Last Revised: 30/12/99