The　frost　crystals　present　needle-like　shapes　and　dendrite　growth　patterns　at　the　initial　period　of　the　frost　formation　on　cold　surfaces.　They　gradually　turn　into　plane-like　shapes　with　time　disappear.　After　frost　crystals　cover　the　whole　cold　surface,　the　frost　formation　steps　into　the　frost　layer　growth　period.　During　this　period,　as　the　frost　layer　becomes　thicker,　its　surface　temperature　can　be　high　enough　to　result　the　frost　crystals　melt　and　fall　down　periodically.　It　is　the　growth　pattern　of　the　frost　crystals　that　results　in　a　multiple-step　ascending　tendency　of　the　fractal　dimension　with　time.　The　physical　meaning　of　the　fractal　dimension　and　the　volume　fraction　in　describing　the　frost　layer　characteristics　are　also　discussed　in　this　paper　and　it　is　pointed　out　that　it　is　necessary　to　introduce　a　fractal　parameter　in　modeling　frost　formation　process.　The　fractal　dimension　may　well　define　the　frost　crystal　shape　and　structure　features;　the　volume　fraction　is　directly　proportional　to　the　frost　layer　density,　and　has　a　very　weak　relation　with　the　frost　crystal　shape　and　structure　features.　(C)　2011　Elsevier　Inc.　All　rights　reserved.