Autre sinus
Formula


This HTML page describes the different parameters you can find in the mde - Autre sinus formula. For further explanations or just suggestions, you may contact me at mdessur@hotmail.com.

I would also mention that English is not my first language. So, I would appreciate comments on how to better this text from that point of view. Thanks.


The formula

I based this formula from my colouring method having the same name and itself a personal version of Mark Townsend's Sinus colouring method.

Here are the parameters for this formula:

Flavour This is a choice of possible behaviours for the colouring method
Choices 1st (default), 2nd, 3rd, 4th, 5th, 6th
Comments 1st corresponds to the cartesian default in Mark's original formula. 6th corresponds to his polar default. The other ones are mine.

 
Horizontal Frequency This parameter has a mathematical meaning. 
Choices Any number is OK. Default is 10.
Comments With the parameter and the next one, you can get shapes that are rectangular instead of square.
It has an effect on the real part of Z (horizontal axis).

 
Horizontal Amplitude This parameter has a mathematical meaning. 
Choices Any number is OK. The default is 0.5.
Comments With the parameter and the previous one, you can get shapes that are rectangular instead of square. This one has also some impacts on colour density.
It has an effect on the real part of Z (horizontal axis).

 
Vertical Frequency This parameter has a mathematical meaning. 
Choices Any number is OK. Default is 10.
Comments With the parameter and the next one, you can get shapes that are rectangular instead of square.
It has an effect on the imaginary part of Z (vertical axis).

 
Vertical Amplitude This parameter has a mathematical meaning. 
Choices Any number is OK. The default is 0.5.
Comments With the parameter and the previous one, you can get shapes that are rectangular instead of square. This one has also some impacts on colour density.
It has an effect on the imaginary part of Z (vertical axis).

 
Power A power can be apply to the formula. A power like the square, the cube, the square root, etc.
Choices You may use any number. 

 
Offset This is just a set of two numbers you may use to start the calculation. Its meaning is purely mathematical.
Choices You may use any number.

 
First, Second, Third Function This is a choice of functions used in the flavours.
Choices All the standard functions you may use in UF parameters. Default is ident for the first two ones and tan for the third one.
Comments This is the way these functions are handled in the flavours that makes the difference among them.
Flavour 1st to 5th use the three functions. Flavour 6th uses only the first two ones.

It also uses the Coordinates Parameter Toolbox, the Barnsley Parameters Toolbox, the Odd-Even Type Parameters Toolbox,  the Epsilon Range Parameter Toolbox, the Bailout Parameters Toolbox and the Function Application (new) Toolbox..