The line connecting rare earth elements (REE) in chondrite-normalised plots can be represented by a smooth polynomial function using lambda shape coefficients as described by O'Neill (2016). In this study, computationally generated lambda combinations are used to construct artificial chondrite-normalised REE patterns that encompass most REE patterns likely to occur in natural materials. The dominant REE per pattern is identified, which would lead to its inclusion in a hypothetical mineral suffix, had this mineral contained essential REE. Furthermore, negative Ce and Y anomalies, common in natural minerals, are considered in the modelled REE patterns to investigate the effect of their exclusion on the relative abundance of the remainder REE. The dominant REE in a mineral results from distinct pattern shapes requiring specific fractionation processes, thus providing information on its genesis. Minerals dominated by heavy lanthanides are rare or non-existent, even though the present analysis shows that REE patterns dominated by Gd, Dy, Er and Yb are geologically plausible. This discrepancy is caused by the inclusion of Y, which dominates heavy REE budgets, in mineral name suffixes. The focus on Y obscures heavy lanthanide mineral diversity and can lead to various fractionation processes to be overlooked. Samarium dominant minerals are known, even though deemed unlikely by the computational model, suggesting additional fractionation processes that are not well described by lambda shape coefficients. Positive Eu anomalies only need to be moderate in minerals depleted in the light REE for Eu to be the dominant REE, thus identifying candidate rocks in which the first Eu dominant mineral might be found. Here, I present an online tool, called ALambdaR that allows interactive control of lambda shape coefficients and visualisation of resulting REE patterns.