Need an Introduction to Tiny Core? Or peruse Core Concepts.
... But it doesn't explain how Busybox, the kernel, and the compiled binaries get merged into a rootfs. ...
mkdir tempdircd tempdirzcat /path/to/existing/rootfs.gz | sudo cpio -i
cd tempdirsudo find . | sudo cpio -o -H newc | gzip > /path/to/new/rootfs.gz