1. An image data processing apparatus which inputs image data generated from an image represented in multiple gradations of dot matrix pixels, diffuses a gradation error for each pixel to the other unconverted pixels, and converts the input image data to image data represented by presence or absence of dot formation, the apparatus comprising: a block process determination unit for forming a block by grouping a specified number of neighboring pixels and determining whether or not a specified block process condition is satisfied on the basis of a gradation value for each pixel in a target block to convert the image data; a first conversion unit for diffusing a gradation error for the entire target block to unconverted pixels outside the target block on the basis of the gradation value and the diffused gradation error for each pixel in the target block and converting image data for pixels in the target block at a time when the block process determination unit determines the block process condition to be true; and a second conversion unit for determining whether or not to form a dot in the target block on the basis of the gradation value and the diffused gradation error for each pixel in the target block when the block process determination unit determines the block process condition to be false, for converting image data for pixels in the target block while diffusing a gradation error for the pixel partition to the other unconverted pixels on the basis of the gradation value and the diffused gradation error for each pixel according to each pixel partition comprising grouped pixels in the target block when it is determined that a dot is to be formed in the target block, and for converting image data for pixels in the target block at a time while diffusing a gradation error for the entire target block to the other unconverted pixels outside the target block on the basis of the gradation value and the diffused gradation error for each pixel in the target block when it is determined that no dot is to be formed in the target block.