# An explicit formula for the pressure of box-like affine iterated function systems

## TL;DR

This paper derives an explicit formula for the pressure function of box-like self-affine fractals, enabling straightforward computation of their affinity dimension and related dimensions, with practical examples included.

## Contribution

It provides a new explicit formula for the pressure function of box-like self-affine sets, simplifying the calculation of their affinity and Hausdorff dimensions.

## Key findings

- Explicit formula for the pressure function derived.
- Simplified computation of affinity dimension demonstrated.
- Examples show ease of calculating fractal dimensions.

## Abstract

In this article we investigate the pressure function and affinity dimension for iterated function systems associated to the "box-like" self-affine fractals investigated by D.-J. Feng, Y. Wang and J.M. Fraser. Combining previous results of V. Yu. Protasov, A. K\"aenm\"aki and the author we obtain an explicit formula for the pressure function which makes it straightforward to compute the affinity dimension of box-like self-affine sets. We also prove a variant of this formula which allows the computation of a modified singular value pressure function defined by J.M. Fraser. We give some explicit examples where the Hausdorff and packing dimensions of a box-like self-affine fractal may be easily computed.