Exponential Sequence

Functionality

This node produces specified number of items from exponential sequence, defined by formula x_n = x0*exp(alpha*n) or x_n = x0*base^n. Obviously, these formulas are equivalent when alpha = log(base).

Sequence can be re-scaled so that maximum of absolute values of produced items will be equal to specified value.

Note. Please do not forget well-known properties of exponential sequences:

• They grow very quickly when base is greater than 1.0 (or alpha greater than 0.0).

• They decrease very quickly when base is less than 1.0 (or alpha less than 0.0).

Inputs & Parameters

All parameters except for Mode can be given by the node or an external input. This node has the following parameters:

Parameter	Type	Default	Description
Mode	Enum: Log or Base	Log	If Log, then x_n = x0*exp(alpha*n). If Base, then x_n = x0*base^n.
X0	Float	1.0	Item of sequence for N=0.
Alpha	Float	0.1	Coefficient in formula exp(alpha*n). Used only in Log mode.
Base	Float	2.0	Exponential base in formula base^n. Used only in Base mode.
N from	Int	0	Minimal value of N.
N to	Int	10	Maximal value of N.
Max	Float	0.0	If non-zero, then all output sequence will be re-scaled so that maximum of absolute values will be equal to number specified.

Outputs

This node has one output: Sequence.

Inputs and outputs are vectorized, so if series of values is passed to one of inputs, then this node will produce several sequences.

Example of usage

Given simplest nodes setup:

you will have something like: