When photographers talk about minimalist images, we often think of compositions where there is lots of space with very simple subjects in the frame. There is a predisposition to thinking more about objects in the frame and one aspect that is often overlooked is that of colour.
Images can be simpler (or quieter) by being very selective about the colour that is used. As a beginner I would often welcome as much colour as I could to my images. When I started out on this road to producing more simplified images, I think I got a handle on the compositional elements within the frame pretty quickly, but one aspect of my compositions that let me down was my use of colour: I knew that something was wrong or missing, and it took me years to realise that sometimes there was simply too much colour.
So if you're looking to simplify your photographs, it's not just about visiting minimalist places, or shooting one or two subjects within the frame. It's also about reducing colour, or being more selective on the amount of colour you use in your work.
I do believe that we all have to go through certain learning stages. The first being to reduce the number of subjects within a frame down to a more coherent assemblage that can support a strong composition. This is really the first stage for many of us. The 2nd stage is to work on the tones contained within the photograph : we are now juggling two balls: object placement and tonal relationships between the objects. And the third stage that comes along at some point is our evaluation of colour. As time goes on, we begin to realise that images can become simpler when we reduce or remove certain subjects with certain colours as they overcomplicate the scene. We also understand that sometimes we don't need a lot of colour for the image to work. In my own case, I sometimes feel I create monochrome images in colour. Some are often reduced down to simple colour palettes of one colour using many shades.
But this can only happy when we are ready. And by being ready, I mean that we are now 'able to see'. I think the reason why I have become more comfortable with reducing the colour palette of my photographs is because my awareness of colour has become more acute over time. Where I would once need to have a colour explosion of saturated hues thrown in my face, I now find it too overwhelming. If I'd tried to reduce the colour palette of my work 10 years ago, I wouldn't have been satisfied because I was still very much in love with the deeply saturated image.
You can't force things. You can only be aware of how your tastes and perception of your visual world is changing, and adjust your work accordingly. That's all you can ask for, and by being sensitive to your own aesthetic changes, and applying them to your work - you move forward.