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The most commonly used coordinate systems are rectangular coordinates and polar coordinates (see polar). But these aren’t the only possibilities. One of the less common coordinate systems is bipolar coordinates. Although their mathematical application is specialized, they can be used in variations to make interesting flames. Rectangular coordinates are based on two families of parallel lines (horizontal and vertical) where each line in the first family intersects each line in the other at a right angle.


The Gateway

Following on with the bTransform on a linear elliptic, I decided to tweak my Splits (painful!) flame a bit more, by adding a bit of blur and altering the parameters a little further.

into the light

I shoot into the light

I decided to make some waves, and spirals branch out. The bTransform did a great job of distorting these into a point, with some added benefits of extra shininess (I think)


bTransform my splits

didn’t have to do much tweaking at all to get the image below. Try it, adjust the bTransform settings, but whole numbers at a time for the best results.


Garden of bTransform

Decided to get a more organic look (totally addicted to that). So went with greens, adjusted a few more settings and parameters to create this foliage tunnel with flowers.

3D without 3D

3D without 3D

I’ve created something using non 3D variations that creates a 3D look, not too dissimilar to the kind of fractal you get with Mandelbulb.