User talk:Emusicster@gmail.com

General Equations for two dimensional functions.

$$x=real (z*(t+d(f(t),t,n)*i)*i^r+a+b*i), y=imag (z*(t+d(f(t),t,n)*i)*i^r+a+b*i)

$$ The above two equations completely define the two dimensional plane for all f(t), so that any f(t) may be zoomed by z, rotated by quadrant r, or translated by a+bi. Further all forms of f(t) obtained by any zoom, rotation, or translation will be similar to the original f(t). Also integrations or derivatives of degree (n) are valid if applied to the original f(t) prior to application of the above equations. If a=0 and b=0 and r=0 and z=1 then f(t) exists in a normal plane. Rotations are achieved by changing the value r from 0 to 4 as the rotation moves from 0 to 360. The possibility of expressing quadrants as partial values is fully defined by this method. The points lying on f(t) take the form of complex coordinates in the form of (x+yi). Translations are performed by adding (a+bi) to (t+f(t)i) thus moving all points to new locations in the plane. In both rotation and translation the similarity of the new (t+f(t)i) to the original f(t) is exactly similar. The z factor may range from - infinity to + infinity. At zero, the function becomes extinct. At negative values of z f(t) is reversed. At positive values f(t) enlarges as z approaches infinity. The same is true for negative values except the effect is completely reversed. This method allows for expression of f(t) in any rotation, zoom, or translation in the original plane, without rotating or distorting the plane in any way. Only the f(t) is changed. The coordinates of points on all similar constructions of f(t) are completely defined, as well as the complex coordinates of f(t) belonging to the plane. Derivatives of f(t) with respect to the variable t in are expressed in degree (n) by the expression: d(f(t),t,n. If n=0 the expression defaults to f(t). Negative (n) yeilds integrals of f(t). (Lyricist 16:19, 3 May 2006 (UTC))