Alpine Linux is a Linux distribution built around musl libc and BusyBox. The image is only 5 MB in size and has access to a package repository that is much more complete than other BusyBox based images. This makes Alpine Linux a great image base for utilities and even production applications. Read more about Alpine Linux here and you can see how their mantra fits in right at home with Docker images.
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Use like you would any other base image:
FROM alpine:3.1
RUN apk add --update mysql-client && rm -rf /var/cache/apk/*
ENTRYPOINT ["mysql"]
This example has a virtual image size of only 16 MB. Compare that to our good friend Ubuntu:
FROM ubuntu:14.04
RUN apt-get update \
&& apt-get install -y mysql-client \
&& rm -rf /var/lib/apt/lists/*
ENTRYPOINT ["mysql"]
This yields us a virtual image size of about 232 MB image.
This image is well documented. Check out the documentation at Viewdocs.