This kind of design is relatively simple, and graphic design software such as Photoshop, CorelDRAW, and IIIustator can all produce such effects.
CorelDRAW and IIIustator are two software commonly used by people in the industry to create logos and logo patterns (the latter can be used in conjunction with Photoshop). LOGO, trademark and other patterns have strict requirements. When the pattern is enlarged many times, it is also required that there is no slight deviation in the pattern. Both software specialize in making vector images for use in printed products. (Vector images will not deviate no matter how many times they are enlarged or reduced. LOGO and logo patterns require simple color effects on the screen. The above two software just meet such requirements.)
Photoshop software can also be used to create this type of image. This software has a wide range of patterns, mostly focusing on picture effects. It can produce pixel images and vector images, but it is not as rigorous as the above two softwares for tasks such as trademarks and LOGO icons.