Firstly, I set up my document with my reference image. Then, I gathered my swatches from the image and organized them in my swatches panel. 

Next, I traced the Coca-Cola logo with the pen tool and added the trademark text with the type on a path tool. 

Here we see the Coca-Cola logo ready to be colored and formatted correctly. 

The Coca-Cola logo has been filled with pure white and no stroke setting. I then used the shape builder tool to cut out the gaps in the type as well as merge complex shapes into cleaner forms. 

To finish up the image, I created the simple circle with the eclipse tool and added a gradient using the swatches I created earlier. On the rightmost Artboard is a copy of the trademark type to permit easy edits if needed. 

The final Coca-Cola logo. An alternative red and white logo was created for versatility. 

I decided to go with the theme of retro movie theaters. Here are some sketches of pattern elements and color exploration. I took inspiration from retro drive-in signage, movie theater carpets, and the vintage ads that would air before films. 

After deciding on the color palette, I used Procreate to experiment with different motifs and shapes that I believed would work for a pattern. I stuck very closely to this mock-up when creating the vector art on Illustrator in the next step. 

Here is the cleaned up vector art and pattern in Adobe Illustrator. 

Next, I took some of the pattern elements to create a new composition with a limited version of the color palette. Before finalizing the patterns, I made some edits to motif sizing and spacing to better the composition. 

Pattern one encapsulates a night out at the movies with the moon and star motifs.

Pattern two is more simplified with a minimalistic version of the color palette.