The air shower arrival time intervals (ASATIs) were observed for several years at five different far-off stations to study the chaotic feature of the cosmic rays. The total number of chaotic time series of ASATIs is 99 from February 1994 to November 2000. The chaotic ASATIs appear six times simultaneously between two different stations, showing a higher probability of simultaneous chaos detection than the random occurrence as implied by the fractal wave pattern of cosmic ray clouds. The average fractal dimension of the fractional chaotic ASATIs for each station is 3.7 +/- 0.1 pm with average duration of 23 h. The distribution of the representative (central) right ascension of air showers among 99 chaotic ASATIs has two peaks around 4 h and 20 h. The time variation of the chaotic feature of the ASATIs for several days shows a quasi-periodic behaviour with the rotation of the earth. These results seem to indicate that the chaotic cosmic rays arrive at the earth, forming wave trains like a fractal pattern which covers an area of the galactic plane surrounding the earth.