# Exponential Sequence¶

*destination after Beta: Number*

## 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.