**Name:** linear

**Type:** 2D

**Name:** linear3D

**Type:** 3D

## Overview

Linear and linear3D are the most basic of the flame fractal variations, performing the identity mapping (passing the input point to the output point). This is the reason linear or linear3D is the default variation for flame fractal programs. (Using no variations at all passes nothing to the output, effectively mapping the plane to a single point, the origin.) Linear is the 2D version and linear3D is the 3D version.

## Parameters

variation amount | Scale factor for the output. 1 is a typical value when linear is used by itself. When used on a transform with other variations, it is usually smaller. |

## Details

Linear and linear3D can be visualized as taking a copy of the overall fractal and transforming it as specified by the pre-affine transform (scaling, rotating, moving, etc.).

When combined with other variations in a transform, linear and linear3D add the scaled values of x, y, and z to the output along with the other variations. The result is dependent on the other variations and the relative amounts of each.

## Special considerations:

In JWildfire, setting Preserve Z makes all variations map z; in this case, linear and linear3D behave the same.

Chaotica is 2D only, but supports the name linear3D so that it can interpret parameters that use it; it works the same a linear in this case.

Apophysis 7X version 15C and later support 3D, but have only linear, which works the same as linear3D. When reading parameters from other programs or versions, it recognizes linear3D and converts it to linear.

## Uses

- Iterated function systems
- Tiling

## Related Variations

linearT, linearT3D, dc_linear

## Mathematics

Linear is the identity function:

(linear3D only)