log4j2 specify relative path to tomcat home dir for FileAppender

I solved my own issue. For system properties you need to prefix variables with sys:.

<FastFile name="ALog" fileName="${sys:catalina.home}/logs/test.log" immediateFlush="true" append="true">
  <PatternLayout>
    <pattern>%d %p %c{1.} [%t] %m%n</pattern>
  </PatternLayout>
</FastFile>

Found it after re-reading this part of the documentation:
http://logging.apache.org/log4j/2.x/manual/configuration.html#PropertySubstitution