# Numerical analysis comparing ODE approach and level set method for evolving spirals by crystalline eikonal-curvature flow

## TL;DR

This paper compares the numerical results of ODE and level set methods for simulating the evolution of crystalline spiral curves, finding minimal differences in their area calculations despite different evolution laws.

## Contribution

It provides a numerical comparison between ODE and level set models for crystalline spiral evolution, highlighting their close agreement in results.

## Key findings

- Small area differences between models
- Differences in evolution laws are minor
- Both methods produce consistent results

## Abstract

In this paper, the evolution of a polygonal spiral curve by the crystalline curvature flow with a pinned center is considered with two view points, discrete model consist of an ODE system of facet lengths and a level set method. We investigate the difference of these models numerically by calculating the area of the region enclosed by these spiral curves. The area difference is calculated by the normalized L1 norm of the difference of step-like functions which are branches of arg(x) whose discontinuities are only on the spirals. We find the differences of the numerical results considered in this paper are very small even though the evolution laws of these models around the center and the farthest facet are slightly different.